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# In this exercise we show that matrix multiplication is ISBN: 9780073383095 37

## Solution for problem 13E Chapter 2.6

Discrete Mathematics and Its Applications | 7th Edition

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Problem 13E

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-by-Step Solution:

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.

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.

Step 3 of 3

##### ISBN: 9780073383095

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