Answer
The statement is correct.
Work Step by Step
Since the matrix $A$ is idempotent, then $A^{2}=A$.
Thus, we have:
$|A|=|A^{2}|=|AA|=|A||A|=|A|^{2}$
Therefore, we see that
$|A|(|A|-1)=0$
This indicates that either $|A|=0$ or $|A|=1$
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 3 - Determinants - 3.3 Properties of Determinants - 3.3 Exercises - Page 127: 80
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