Answer
True
Work Step by Step
Consider a diagonalizable matrix $A$:
$S^{-1}AS=D$
then $D^2=(S^{-1}AS)^2=(S^{-1}AS)(S^{-1}AS)=S^{-1}A^2S$
Hence, $A^2$ is also diagonalizable.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 7 - Eigenvalues and Eigenvectors - 7.3 Diagonalization - True-False Review - Page 459: f
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