Program to multiply two matrices - GeeksforGeeks

02 Mar, 2022
Given two matrices, the task to multiply them. Matrices can either be square or rectangular.
Examples: 
(Square Matrix Multiplication)
Input : mat1[m][n] = {
             {1, 1},
            {2, 2}
        }
        mat2[n][p] = {
            {1, 1},
            {2, 2}
        }
Output : result[m][p] = {
             {3, 3},
            {6, 6}
         }

(Rectangular Matrix Multiplication)
Input : mat1[3][2] = {
             {1, 1},
            {2, 2},
            {3, 3}
        }
        mat2[2][3] = {
            {1, 1, 1},
            {2, 2, 2}
        }
Output : result[3][3] = {
             {3, 3, 3},
            {6, 6, 6},
            {9, 9, 9}
         }
Multiplication of two Square or Rectangular Matrices:
This program can multiply any two square or rectangular matrices.
The below program multiplies two square matrices of size 4 * 4.
There is also an example of a rectangular matrix for the same code (commented below).
We can change the Matrix value with the number of rows and columns (from MACROs) for Matrix-1 and Matrix-2 for different dimensions.
Note:  i-  The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2.
           ii-  Output of multiplication of Matrix-1 and Matrix-2, results with equal to the number of rows of Matrix-1 and 
                 the number of columns of Matrix-2 i.e. rslt[R1][C2].
C++
C
/* * This C++ program can multiply any two square or rectangular matrices. * The below program multiplies two square matrices of size 4 * 4. * There is also an example of a rectangular matrix for the same code (commented below). * We can change the Matrix value with the number of rows and columns (from MACROs) for Matrix-1 * and Matrix-2 for different dimensions. */ /* * Note:  i- The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2. *       ii- Output of multiplication of Matrix-1 and Matrix-2, results with equal to the number *           of rows of Matrix-1 and the number of columns of Matrix-2 i.e. rslt[R1][C2]. */ #include <iostream> using namespace std; // Edit MACROs here, according to your Matrix Dimensions for mat1[R1][C1] and mat2[R2][C2]#define R1 4            // number of rows in Matrix-1#define C1 4            // number of columns in Matrix-1#define R2 4            // number of rows in Matrix-2#define C2 4            // number of columns in Matrix-2 void mulMat(int mat1[][C1], int mat2[][C2]) {    int rslt[R1][C2];     cout << "Multiplication of given two matrices is:\n" << endl;     for (int i = 0; i < R1; i++) {        for (int j = 0; j < C2; j++) {            rslt[i][j] = 0;             for (int k = 0; k < R2; k++) {                rslt[i][j] += mat1[i][k] * mat2[k][j];            }             cout << rslt[i][j] << "\t";        }         cout << endl;    }} int main(void) {    // Square Matrices    // R1 = 4, C1 = 4 and R2 = 4, C2 = 4 (Update these values in MACROs)    int mat1[R1][C1] = {            {1, 1, 1, 1},            {2, 2, 2, 2},            {3, 3, 3, 3},            {4, 4, 4, 4}    };     int mat2[R2][C2] = {            {1, 1, 1, 1},            {2, 2, 2, 2},            {3, 3, 3, 3},            {4, 4, 4, 4}    };     /*    // Rectangular Matrices    // R1 = 3, C1 = 4 and R2 = 4, C2 = 3 (Update these values in MACROs)    int mat1[R1][C1] = {                {1, 1, 1, 1},                {2, 2, 2, 2},                {3, 3, 3, 3}    };     int mat2[R2][C2] = {                {1, 1, 1},                {2, 2, 2},                {3, 3, 3},                {4, 4, 4}    };    */     if (C1 != R2) {        cout << "The number of columns in Matrix-1  must be equal to the number of rows in "                "Matrix-2" << endl;        cout << "Please update MACROs according to your array dimension in #define section"                << endl;         exit(EXIT_FAILURE);    }     mulMat(mat1, mat2);     return 0;} // This code is contributed by Manish Kumar (mkumar2789)
/* * This C program can multiply any two square or rectangular matrices. * The below program multiplies two square matrices of size 4 * 4. * There is also an example of a rectangular matrix for the same code (commented below). * We can change the Matrix value with the number of rows and columns (from MACROs) for Matrix-1 * and Matrix-2 for different dimensions. */ /* * Note:  i- The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2. *       ii- Output of multiplication of Matrix-1 and Matrix-2, results with equal to the number *           of rows of Matrix-1 and the number of columns of Matrix-2 i.e. rslt[R1][C2]. */ #include <stdio.h>#include <stdlib.h> // Edit MACROs here, according to your Matrix Dimensions for mat1[R1][C1] and mat2[R2][C2]#define R1 4            // number of rows in Matrix-1#define C1 4            // number of columns in Matrix-1#define R2 4            // number of rows in Matrix-2#define C2 4            // number of columns in Matrix-2 void mulMat(int mat1[][C1], int mat2[][C2]) {    int rslt[R1][C2];     printf("Multiplication of given two matrices is:\n\n");     for (int i = 0; i < R1; i++) {        for (int j = 0; j < C2; j++) {            rslt[i][j] = 0;             for (int k = 0; k < R2; k++) {                rslt[i][j] += mat1[i][k] * mat2[k][j];            }             printf("%d\t", rslt[i][j]);        }         printf("\n");    }} int main(void) {    // Square Matrices    // R1 = 4, C1 = 4 and R2 = 4, C2 = 4 (Update these values in MACROs)    int mat1[R1][C1] = {            {1, 1, 1, 1},            {2, 2, 2, 2},            {3, 3, 3, 3},            {4, 4, 4, 4}    };     int mat2[R2][C2] = {            {1, 1, 1, 1},            {2, 2, 2, 2},            {3, 3, 3, 3},            {4, 4, 4, 4}    };     /*    // Rectangular Matrices    // R1 = 3, C1 = 4 and R2 = 4, C2 = 3 (Update these values in MACROs)    int mat1[R1][C1] = {            {1, 1, 1, 1},            {2, 2, 2, 2},            {3, 3, 3, 3}    };     int mat2[R2][C2] = {            {1, 1, 1},            {2, 2, 2},            {3, 3, 3},            {4, 4, 4}    };    */     if (C1 != R2) {        printf("The number of columns in Matrix-1  must be equal to the number of rows in "                "Matrix-2\n");        printf("Please update MACROs value according to your array dimension in "                "#define section\n");         exit(EXIT_FAILURE);    }     mulMat(mat1, mat2);     return 0;} // This code is contributed by Manish Kumar (mkumar2789)
Multiplication of given two matrices is:

10    10    10    10    
20    20    20    20    
30    30    30    30    
40    40    40    40    
Multiplication of Square Matrices : The below program multiplies two square matrices of size 4*4, we can change N for different dimensions. 
C++
C
Java
Python3
C#
PHP
Javascript
// C++ program to multiply// two square matrices.#include <iostream> using namespace std; #define N 4 // This function multiplies// mat1[][] and mat2[][], and// stores the result in res[][]void multiply(int mat1[][N],              int mat2[][N],              int res[][N]){    int i, j, k;    for (i = 0; i < N; i++) {        for (j = 0; j < N; j++) {            res[i][j] = 0;            for (k = 0; k < N; k++)                res[i][j] += mat1[i][k] * mat2[k][j];        }    }} // Driver Codeint main(){    int i, j;    int res[N][N]; // To store result    int mat1[N][N] = { { 1, 1, 1, 1 },                       { 2, 2, 2, 2 },                       { 3, 3, 3, 3 },                       { 4, 4, 4, 4 } };     int mat2[N][N] = { { 1, 1, 1, 1 },                       { 2, 2, 2, 2 },                       { 3, 3, 3, 3 },                       { 4, 4, 4, 4 } };     multiply(mat1, mat2, res);     cout << "Result matrix is \n";    for (i = 0; i < N; i++) {        for (j = 0; j < N; j++)            cout << res[i][j] << " ";        cout << "\n";    }     return 0;} // This code is contributed// by Soumik Mondal
// C program to multiply two square matrices.#include <stdio.h>#define N 4 // This function multiplies mat1[][] and mat2[][],// and stores the result in res[][]void multiply(int mat1[][N], int mat2[][N], int res[][N]){    int i, j, k;    for (i = 0; i < N; i++) {        for (j = 0; j < N; j++) {            res[i][j] = 0;            for (k = 0; k < N; k++)                res[i][j] += mat1[i][k] * mat2[k][j];        }    }} int main(){    int mat1[N][N] = { { 1, 1, 1, 1 },                       { 2, 2, 2, 2 },                       { 3, 3, 3, 3 },                       { 4, 4, 4, 4 } };     int mat2[N][N] = { { 1, 1, 1, 1 },                       { 2, 2, 2, 2 },                       { 3, 3, 3, 3 },                       { 4, 4, 4, 4 } };     int res[N][N]; // To store result    int i, j;    multiply(mat1, mat2, res);     printf("Result matrix is \n");    for (i = 0; i < N; i++) {        for (j = 0; j < N; j++)            printf("%d ", res[i][j]);        printf("\n");    }     return 0;}
// Java program to multiply two square// matrices.import java.io.*; class GFG {     static int N = 4;     // This function multiplies mat1[][]    // and mat2[][], and stores the result    // in res[][]    static void multiply(int mat1[][],                         int mat2[][], int res[][])    {        int i, j, k;        for (i = 0; i < N; i++) {            for (j = 0; j < N; j++) {                res[i][j] = 0;                for (k = 0; k < N; k++)                    res[i][j] += mat1[i][k]                                 * mat2[k][j];            }        }    }     // Driver code    public static void main(String[] args)    {        int mat1[][] = { { 1, 1, 1, 1 },                         { 2, 2, 2, 2 },                         { 3, 3, 3, 3 },                         { 4, 4, 4, 4 } };         int mat2[][] = { { 1, 1, 1, 1 },                         { 2, 2, 2, 2 },                         { 3, 3, 3, 3 },                         { 4, 4, 4, 4 } };         // To store result        int res[][] = new int[N][N];        int i, j;        multiply(mat1, mat2, res);         System.out.println("Result matrix"                           + " is ");        for (i = 0; i < N; i++) {            for (j = 0; j < N; j++)                System.out.print(res[i][j]                                 + " ");            System.out.println();        }    }} // This code is contributed by anuj_67.
# 4x4 matrix multiplication using Python3# Function definitiondef matrix_multiplication(M, N):    # List to store matrix multiplication result    R = [[0, 0, 0, 0],        [0, 0, 0, 0],        [0, 0, 0, 0],        [0, 0, 0, 0]]     for i in range(0, 4):        for j in range(0, 4):            for k in range(0, 4):                R[i][j] += M[i][k] * N[k][j]     for i in range(0, 4):        for j in range(0, 4):            # if we use print(), by default cursor moves to next line each time,            # Now we can explicitly define ending character or sequence passing            # second parameter as end ="<character or string>"            # syntax: print(<variable or value to print>, end ="<ending with>")            # Here space (" ") is used to print a gap after printing            # each element of R            print(R[i][j], end =" ")        print("\n", end ="") # First matrix. M is a listM = [[1, 1, 1, 1],    [2, 2, 2, 2],    [3, 3, 3, 3],    [4, 4, 4, 4]] # Second matrix. N is a listN = [[1, 1, 1, 1],    [2, 2, 2, 2],    [3, 3, 3, 3],    [4, 4, 4, 4]]     # Call matrix_multiplication functionmatrix_multiplication(M, N) # This code is contributed by Santanu
// C# program to multiply two square// matrices.using System; class GFG {     static int N = 4;     // This function multiplies mat1[][]    // and mat2[][], and stores the result    // in res[][]    static void multiply(int[, ] mat1,                         int[, ] mat2, int[, ] res)    {        int i, j, k;        for (i = 0; i < N; i++) {            for (j = 0; j < N; j++) {                res[i, j] = 0;                for (k = 0; k < N; k++)                    res[i, j] += mat1[i, k]                                 * mat2[k, j];            }        }    }     // Driver code    public static void Main()    {        int[, ] mat1 = { { 1, 1, 1, 1 },                         { 2, 2, 2, 2 },                         { 3, 3, 3, 3 },                         { 4, 4, 4, 4 } };         int[, ] mat2 = { { 1, 1, 1, 1 },                         { 2, 2, 2, 2 },                         { 3, 3, 3, 3 },                         { 4, 4, 4, 4 } };         // To store result        int[, ] res = new int[N, N];        int i, j;        multiply(mat1, mat2, res);         Console.WriteLine("Result matrix"                          + " is ");        for (i = 0; i < N; i++) {            for (j = 0; j < N; j++)                Console.Write(res[i, j]                              + " ");            Console.WriteLine();        }    }} // This code is contributed by anuj_67.
<?php// PHP program to multiply two// square matrices. // This function multiplies mat1[][] and// mat2[][], and stores the result in res[][]function multiply(&$mat1, &$mat2, &$res){    $N = 4;    for ($i = 0; $i < $N; $i++)    {        for ($j = 0; $j < $N; $j++)        {            $res[$i][$j] = 0;            for ($k = 0; $k < $N; $k++)                $res[$i][$j] += $mat1[$i][$k] *                                $mat2[$k][$j];        }    }} // Driver Code$mat1 = array(array(1, 1, 1, 1),              array(2, 2, 2, 2),              array(3, 3, 3, 3),              array(4, 4, 4, 4)); $mat2 = array(array(1, 1, 1, 1),              array(2, 2, 2, 2),              array(3, 3, 3, 3),              array(4, 4, 4, 4)); multiply($mat1, $mat2, $res);$N = 4;echo ("Result matrix is \n");for ($i = 0; $i < $N; $i++){    for ($j = 0; $j < $N; $j++)    {        echo ($res[$i][$j]);        echo(" ");    }    echo ("\n");} // This code is contributed// by Shivi_Aggarwal?>
<script> // Javascript program to multiply// two square matrices. const N = 4; // This function multiplies// mat1[][] and mat2[][], and// stores the result in res[][]function multiply(mat1, mat2, res){    let i, j, k;    for (i = 0; i < N; i++) {        for (j = 0; j < N; j++) {            res[i][j] = 0;            for (k = 0; k < N; k++)                res[i][j] += mat1[i][k] * mat2[k][j];        }    }} // Driver Code    let i, j;         // To store result    let res = new Array(N);    for (let k = 0; k < N; k++)        res[k] = new Array(N);             let mat1 = [ [ 1, 1, 1, 1 ],                       [ 2, 2, 2, 2 ],                       [ 3, 3, 3, 3 ],                       [ 4, 4, 4, 4 ] ];     let mat2 = [ [ 1, 1, 1, 1 ],                       [ 2, 2, 2, 2 ],                       [ 3, 3, 3, 3 ],                       [ 4, 4, 4, 4 ] ];     multiply(mat1, mat2, res);     document.write("Result matrix is <br>");    for (i = 0; i < N; i++) {        for (j = 0; j < N; j++)            document.write(res[i][j] + " ");        document.write("<br>");    } </script>
Result matrix is 
10 10 10 10 
20 20 20 20 
30 30 30 30 
40 40 40 40 
Time complexity: O(n3). It can be optimized using Strassen’s Matrix Multiplication
Auxiliary Space: O(n2)
Multiplication of Rectangular Matrices : We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.How to pass a 2D array as a parameter in C? 
C++
C
Java
Python3
C#
PHP
Javascript
// C++ program to multiply two// rectangular matrices#include <bits/stdc++.h>using namespace std; // Multiplies two matrices mat1[][]// and mat2[][] and prints result.// (m1) x (m2) and (n1) x (n2) are// dimensions of given matrices.void multiply(int m1, int m2, int mat1[][2], int n1, int n2,              int mat2[][2]){    int x, i, j;    int res[m1][n2];    for (i = 0; i < m1; i++)    {        for (j = 0; j < n2; j++)        {            res[i][j] = 0;            for (x = 0; x < m2; x++)            {                *(*(res + i) + j) += *(*(mat1 + i) + x)                                     * *(*(mat2 + x) + j);            }        }    }    for (i = 0; i < m1; i++)    {        for (j = 0; j < n2; j++)        {            cout << *(*(res + i) + j) << " ";        }        cout << "\n";    }} // Driver codeint main(){    int mat1[][2] = { { 2, 4 }, { 3, 4 } };    int mat2[][2] = { { 1, 2 }, { 1, 3 } };    int m1 = 2, m2 = 2, n1 = 2, n2 = 2;       // Function call    multiply(m1, m2, mat1, n1, n2, mat2);    return 0;} // This code is contributed// by Akanksha Rai(Abby_akku)
// C program to multiply two rectangular matrices#include <stdio.h> // Multiplies two matrices mat1[][] and mat2[][]// and prints result.// (m1) x (m2) and (n1) x (n2) are dimensions// of given matrices.void multiply(int m1, int m2, int mat1[][m2], int n1,              int n2, int mat2[][n2]){    int x, i, j;    int res[m1][n2];    for (i = 0; i < m1; i++)    {        for (j = 0; j < n2; j++)        {            res[i][j] = 0;            for (x = 0; x < m2; x++)            {                *(*(res + i) + j) += *(*(mat1 + i) + x)                                     * *(*(mat2 + x) + j);            }        }    }    for (i = 0; i < m1; i++)    {        for (j = 0; j < n2; j++)        {            printf("%d ", *(*(res + i) + j));        }        printf("\n");    }} // Driver codeint main(){    int mat1[][2] = { { 2, 4 }, { 3, 4 } };    int mat2[][2] = { { 1, 2 }, { 1, 3 } };    int m1 = 2, m2 = 2, n1 = 2, n2 = 2;       // Function call    multiply(m1, m2, mat1, n1, n2, mat2);    return 0;}
// Java program to multiply two matrices. public class GFG{     /**     * to find out matrix multiplication     *     * @param matrix1 First matrix     * @param rows1   Number of rows in matrix 1     * @param cols1   Number of columns in matrix 1     * @param matrix2 Second matrix     * @param rows2   Number of rows in matrix 2     * @param cols2   Number of columns in matrix 2     * @return the result matrix (matrix 1 and matrix 2     * multiplication)     */    public static int[][] matrixMultiplication(        int[][] matrix1, int rows1, int cols1,        int[][] matrix2, int rows2, int cols2)        throws Exception    {         // Required condition for matrix multiplication        if (cols1 != rows2) {            throw new Exception("Invalid matrix given.");        }         // create a result matrix        int resultMatrix[][] = new int[rows1][cols2];         // Core logic for 2 matrices multiplication        for (int i = 0; i < resultMatrix.length; i++)        {            for (int j = 0;                 j < resultMatrix[i].length;                 j++)            {                for (int k = 0; k < cols1; k++)                {                    resultMatrix[i][j]                        += matrix1[i][k] * matrix2[k][j];                }            }        }        return resultMatrix;    }     // Driver code    public static void main(String[] args) throws Exception    {         // Initial matrix 1 and matrix 2        int matrix1[][] = { { 2, 4 }, { 3, 4 } };        int matrix2[][] = { { 1, 2 }, { 1, 3 } };         // Function call to get a matrix multiplication        int resultMatrix[][] = matrixMultiplication(            matrix1, 2, 2, matrix2, 2, 2);         // Display result matrix        System.out.println("Result Matrix is:");        for (int i = 0; i < resultMatrix.length; i++)        {            for (int j = 0;                 j < resultMatrix[i].length;                 j++)            {                System.out.print(resultMatrix[i][j] + "\t");            }            System.out.println();        }    }    // This code is contributed by darshatandel1998 (Darshan    // Tandel)}
# Python3 program to multiply two# rectangular matrices # Multiplies two matrices mat1[][]# and mat2[][] and prints result.# (m1) x (m2) and (n1) x (n2) are# dimensions of given matrices.def multiply(m1, m2, mat1,             n1, n2, mat2):     res = [[0 for x in range(n2)]              for y in range (m1)]         for i in range(m1):        for j in range(n2):            res[i][j] = 0            for x in range(m2):                           res[i][j] += (mat1[ i][x] *                              mat2[ x][j])                for i in range(m1):        for j in range(n2):                 print (res[i][j],                   end = " ")               print () # Driver codeif __name__ == "__main__":       mat1 = [[2, 4], [3, 4]]    mat2 = [[1, 2], [1, 3]]    m1, m2, n1, n2 = 2, 2, 2, 2       # Function call    multiply(m1, m2, mat1,             n1, n2, mat2)     # This code is contributed by Chitranayal
// C# program to multiply two// rectangular matricesusing System; class GFG{     // Multiplies two matrices mat1[][]// and mat2[][] and prints result.// (m1) x (m2) and (n1) x (n2) are// dimensions of given matrices.static void multiply(int m1, int m2, int[,] mat1,                     int n1, int n2, int[,] mat2){    int x, i, j;    int[,] res = new int[m1, n2];         for(i = 0; i < m1; i++)    {        for(j = 0; j < n2; j++)        {            res[i, j] = 0;                         for(x = 0; x < m2; x++)            {                res[i, j] += (mat1[i, x] *                              mat2[x, j]);            }        }    }    for(i = 0; i < m1; i++)    {        for(j = 0; j < n2; j++)        {            Console.Write(res[i, j] + " ");        }        Console.WriteLine();    }} // Driver Codestatic void Main(){    int[,] mat1 = { { 2, 4 }, { 3, 4 } };    int[,] mat2 = { { 1, 2 }, { 1, 3 } };    int m1 = 2, m2 = 2, n1 = 2, n2 = 2;         // Function call    multiply(m1, m2, mat1, n1, n2, mat2);}} // This code is contributed by divyeshrabadiya07
<?php// PHP program to multiply two// rectangular matrices // Multiplies two matrices mat1[][] // and mat2[][] and prints result.// (m1) x (m2) and (n1) x (n2) are// dimensions of given matrices.function multiply($m1, $m2, $mat1,                  $n1, $n2, $mat2){    for ($i = 0; $i < $m1; $i++)    {        for ($j = 0; $j < $n2; $j++)        {            $res[$i][$j] = 0;            for ($x = 0; $x < $m2; $x++)            {                $res[$i][$j] += $mat1[$i][$x] *                                $mat2[$x][$j];            }        }    }    for ($i = 0; $i < $m1; $i++)    {        for ($j = 0; $j < $n2; $j++)        {            echo $res[$i][$j] . " ";        }        echo "\n";    }} // Driver code$mat1 = array( array( 2, 4 ), array( 3, 4 ));$mat2 = array( array( 1, 2 ), array( 1, 3 ));$m1 = 2;$m2 = 2;$n1 = 2;$n2 = 2; //Function callmultiply($m1, $m2, $mat1, $n1, $n2, $mat2); // This code is contributed by rathbhupendra?>
<script> // Javascript program to multiply two// rectangular matrices // Multiplies two matrices mat1[][]// and mat2[][] and prints result.// (m1) x (m2) and (n1) x (n2) are// dimensions of given matrices.function multiply(m1, m2, mat1, n1, n2, mat2){    let x, i, j;    let res = new Array(m1);    for (i = 0; i < m1; i++)        res[i] = new Array(n2);             for (i = 0; i < m1; i++)    {        for (j = 0; j < n2; j++)        {            res[i][j] = 0;            for (x = 0; x < m2; x++)            {                res[i][j] += mat1[i][x] * mat2[x][j];            }        }    }    for (i = 0; i < m1; i++)    {        for (j = 0; j < n2; j++)        {            document.write(res[i][j] + " ");        }        document.write("<br>");    }} // Driver code    let mat1 = [ [ 2, 4 ], [ 3, 4 ] ];    let mat2 = [ [ 1, 2 ], [ 1, 3 ] ];    let m1 = 2, m2 = 2, n1 = 2, n2 = 2;       // Function call    multiply(m1, m2, mat1, n1, n2, mat2);     </script>
6 16 
7 18 
Time complexity: O(n3). It can be optimized using Strassen’s Matrix Multiplication
Auxiliary Space: O(m1 * n2)
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