   Chapter 1.6, Problem 9E

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Textbook Problem
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# Find two square matrices A and B such that A B ≠ B A .

To determine

Two square matrices A and B such that ABBA

Explanation

Formula used:

Definition: Matrix multiplication

The product of m×n matrix A over and n×p matrix B over is m×p matrix C=AB, where the element cij in row i and column j of AB is found by using the elements in row i of A, and the elements in column j of B in the following manner:

columnjofBcolumnjofCrowiofA[ai1ai2ai3ain][b1jb2jb3jbnj]=[cij]rowiofC

Where cij=ai1b1j+ai2b2j++ainbnj.

Calculation:

Let A= and B=

These two matrices are square matrices of order 2

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