We now need to discuss matrix determinant and matrix inverse. Check this is true by multuplying any matrix times I . A 21 for example is defined as The way to get the matrix elements appearing in this determinant is just by crossing out the rows and columns in which A 21 appears in matrix A and the elements left over go into the cofactor. Finally we get to the matrix inverse. Find the inverse of and check your answer.
Solution Let's write .
Notice that the determinant in the cofactor is just a single number for matrices. The other cofactors are . Thus we are now sure that our calculation of A -1 is correct. Also having verified this gives justification for believing in all the formulas for cofactors and inverse given above.