Answer
See solution
Work Step by Step
If $A^2$ is the zero matrix, $A^2x=0$. However,
$A^2x=AAx=A\lambda x=\lambda Ax=\lambda^2x=0$. Because x is a nonzero vector, $\lambda$ must be 0.
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 5 - Eigenvalues and Eigenvectors - 5.1 Exercises - Page 274: 26
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