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Q39E

Expert-verified

Found in: Page 108

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

If matrices A and B commute, then the formula A²B = BA² must hold.

The statement is true.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Explaining

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

$A^{2} B = A (AB) = A (BA) = (AB) A = (BA) A = B (AA) = {BA}^{2}$

Step 2: Result

Thus the statement is true.

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