   Chapter 10.2, Problem 11ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Give an example different from that in the text to show that matrix multiplication is not commutative. That is, find 2 × 2 matrices A and B such that AB and BA both exist but A B ≠ B A .

To determine

Give an example different from that in the text to show that matrix multiplication is not commutative. That is, find 2 x 2 matrices A and B such that AB and BA both exists but ABBA.

Explanation

Given information:

2 × 2 matrices A and B such that AB and BA both exists but ABBA.

Calculation:

For example, let us choose the following two 2 x 2-matrices:

A = [ 1 2 3 4]B = [ 2 1 4 3]

The first matrix has dimensions 2 × 2 and the second matrix has dimension 2 × 2. Since the inner dimensions are equal, we can multiply the matrices. Moreover, the product should be a

2 × 2-matrix.

Multiplying the rows of the first matrix with the columns of the second matrix (adding the products of the corresponding elements):

AB =

=[ 12+24 11+23 32+44 31+43]=[ 2+8 1+6 6+16 3+12]=[ 10 7 22

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