In this exercise we show that matrix multiplication is associative. Suppose that A is an m × p matrix, B is a p × k matrix, and C is a k × n matrix. Show that A(BC) = (AB)C.

Step 1:

In this problem,we have to show that matrix multiplication is associative. Show that A(BC) = (AB)C

Step 2:

Suppose that A is an m × p matrix, B is a p × k matrix, and C is a k × n matrix.

As we know about

matrix multiplication:

Let assume A=[aij] is a matrix of the size c x d and B=[bij] is a matrix of r x s. Then the product AB=[cij] is a matrix size c x s

Condition:

The number of columns (d) of A matrix must be equal to the number of rows (r) of matrix B, then the product AB is valid.The number of rows of AB matrix is equal to same as the row (c) of A matrix and number of columns of AB is same as (r) of B.Finally we can say that AB matrix size (c x s) equal to same row in matrix A and same columns in matrix B.