Answer
See explanation
Work Step by Step
Let $(I-A)^{-1}=I+A+A^{2}+\cdots+A^{n-1}$
Let's show that this is inverse.
$(I-A)\left(I+A+A^{2}+\cdots+A^{n-1}\right)=$
$=I+A+A^{2}+\cdots+A^{n-1}-A-A^{2}-\cdots-A^{n-1}-A^{n}=I$
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: 4
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