Answer
See the proof below.
Work Step by Step
Since $A^{2}=A$, then $|A^{2}|=|A| |A|=|A|$ and thus
$(I-2A)(I-2A)=I^{2}-2IA-2AI+4A^{2}=I-2A-2A+4A=I-4A+4A=I$
Therefore,
$(I-2A)=(I-2A)^{-1}$
Elementary Linear Algebra 7th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
1-13311-087-8
ISBN 13:
978-1-13311-087-3
Chapter 2 - Matrices - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 73: 69
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