matrix multiplication implemented in python from scratch without arrays.

matrix-multiplication.py

def matrix_multiplication(A, B):
    m = len(A)
    n = len(A[0])

    n2 = len(B)
    k = len(B[0])

    assert n == n2
    assert all(len(row)==n for row in A)
    assert all(len(row)==k for row in B)

    matrix = []
    for i in range(m):
        row = []

        for j in range(k):
            row.append(
                sum(
                    A[i][c] * B[c][j]
                    for c in range(n)
                )
            )

        matrix.append(row)

    return matrix


if __name__ == "__main__":
    from pprint import pprint

    A = [
        [1, 2],
        [1, 3]
    ]

    B = [
        [1, 0],
        [0, 1]
    ]

    print('A:')
    pprint(A)
    print()

    print('B:')
    pprint(B)
    print()

    print('A.B:')
    pprint(matrix_multiplication(A, B))
    print()

    print('B.A:')
    pprint(matrix_multiplication(B, A))