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Expert-verified Found in: Page 108 ### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974 # If matrices A and B commute, then the formula A2B = BA2 must hold.

The statement is true.

See the step by step solution

## Step 1: Explaining

The claim is that if A and B commute then ${\mathrm{A}}^{2}\mathrm{B}={\mathrm{BA}}^{2}$ . First by definition if A and B commute this means that thus we will have:

${\mathrm{A}}^{2}\mathrm{B}=\mathrm{A}\left(\mathrm{AB}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{A}\left(\mathrm{BA}\right)\phantom{\rule{0ex}{0ex}}=\left(\mathrm{AB}\right)\mathrm{A}\phantom{\rule{0ex}{0ex}}=\left(\mathrm{BA}\right)\mathrm{A}\phantom{\rule{0ex}{0ex}}=\mathrm{B}\left(\mathrm{AA}\right)\phantom{\rule{0ex}{0ex}}={\mathrm{BA}}^{2}$

## Step 2: Result

Thus the statement is true. ### Want to see more solutions like these? 