Answer
See solution
Work Step by Step
$A^{2}-2 A+I=0$
$A^{2}=2 A-I,$ multiply with $A$
$A^{3}=2 A^{2}-A=2(2 A-I)-A=4 A-2 I-A=3 A-2 I,$ multiply
with $A$
$A^{4}=3 A^{2}-2 A=3(2 A-I)-2 A=6 A-3 I-2 A=4 A-3 I$
Linear Algebra and Its Applications (5th Edition)
by Lay, David C.; Lay, Steven R.; McDonald, Judi J.
Published by
Pearson
ISBN 10:
032198238X
ISBN 13:
978-0-32198-238-4
Chapter 2 - Matrix Algebra - Supplementary Exercises - Page 162: 5
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