Question

Explain closure, associative, multiplicative and distributive properties of multiplication of matrices.

Answer 1

Two matrices are said to be conformable for multiplication if the number of columns of the first matrix is equal to the number of rows of the second matrix.

Closure Property: If A and B are two matrices, then AB is also a matrix.

Associative property: Suppose A, B, C are matrices. If AB and (AB)C are defined, BC and A(BC) are defined, then (AB)C = A(BC)

Multiplicative Identity: If A and I are square matrices of the same order, then AI = IA = A

Distributive property: Matrix multiplication is distributive with respect to matrix addition.

i.e. A. (B + C) = A . B + A . C