# Problem Description
This appears to be a matrix validation problem where we need to check if a given MxN matrix follows certain rules related to horizontal (H-flip) and vertical (V-flip) transformations. A matrix is considered valid if it maintains certain properties after these transformations.

# Visual Facts
1. Each example shows a MxN matrix and its transformations:
   - H-flip (horizontal flip)
   - V-flip (vertical flip)

2. Example 1 shows a valid case where:
   - Both H-flip and V-flip transformations result in "same" comparisons
   - The matrix contains only numbers 1 and 3

3. Examples 2 and 3 show invalid cases where:
   - At least one of the transformations results in "different" comparisons
   - These matrices contain numbers 1, 2, 3, and 4

4. Each matrix is compared with two reference patterns on the right

5. The transformations are marked with arrows:
   - Orange arrows show the flip direction
   - Green dotted arrows indicate "same" comparison
   - Red dotted arrows indicate "different" comparison

# Visual Patterns
1. Symmetry Rules:
   - For a valid matrix, both H-flip and V-flip should result in the same pattern as the original matrix
   - When a matrix is flipped, corresponding positions should contain the same numbers

2. Structure Patterns:
   - The matrices appear to have a specific structure:
     * Corner positions contain the same number (in valid case)
     * Middle edges contain another number
     * Center position contains a different number

3. Valid Matrix Properties:
   - In the valid example (Example 1):
     * Corners all contain 1
     * Middle edges contain 3
     * Center contains 1
     * Perfect symmetry is maintained in both horizontal and vertical flips

4. Validation Rule:
   - A matrix is valid only if BOTH:
     * Horizontal flip maintains the same pattern
     * Vertical flip maintains the same pattern


# Solution
from typing import List

def solution(matrix: List[List[int]]) -> bool:
    """
    Validates whether the given matrix follows the rules shown in the image.

    Parameters:
        matrix (List[List[int]]): Matrix to be validated. (M*N matrix)

    Returns:
        bool: True if the matrix is valid, False otherwise.
    """
    for row in matrix:
        if row != row[::-1]:
            return False

    for col in range(len(matrix[0])):
        col_values = [matrix[row][col] for row in range(len(matrix))]
        if col_values != col_values[::-1]:
            return False

    return True


# Test Script
def test():
    test_cases = [
        ([[1]], True),
        ([[1, 2, 3]], False),
        ([[1], [2], [1]], True),
        ([[1, 2, 1], [2, 3, 2], [1, 2, 1]], True),
        ([[1, 2, 3], [2, 4, 2], [1, 2, 3]], False),
        ([[1, 2], [2, 1]], False),
        ([[1, 3, 1], [3, 4, 3], [1, 3, 1]], True),
        ([[1, 2, 3, 2, 1], [2, 3, 4, 3, 2], [3, 4, 5, 4, 3], [2, 3, 4, 3, 2], [1, 2, 3, 2, 1]], True),
        ([[1, 2, 3, 2, 1], [4, 3, 4, 3, 2], [3, 4, 6, 1, 3], [2, 3, 4, 3, 2], [1, 2, 3, 2, 1]], False), 
        ([[1, 2, 2, 1], [3, 4, 4, 3], [3, 4, 4, 3], [1, 2, 2, 1]], True),
    ]

    for matrix, expected_output in test_cases:
        try:
            output = solution(matrix)
        except Exception as e:
            error_message = (
                f"An exception occurred while running the test case:\n"
                f"`matrix`: {matrix}\n\n"
                f"Exception: '{str(e)}'"
            )
            assert False, error_message

        if output != expected_output:
            error_message = (
                f"The following Test Case failed:\n"
                f"`matrix`: {matrix}\n\n"
                f"Actual Output: {output}\n"
                f"Expected Output: {expected_output}"
            )
            assert False, error_message

test()