Answer
True
Work Step by Step
Let $A$ be a $2 \times 2$ matrix, and $B=\begin{bmatrix}
1 & 1\\
0 & 1
\end{bmatrix}$
then $A^2=B^2=I_{2 \times 2}$ but we can see $A$ and $B$ are not similar.
Then, the statement is not true.
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 - 7.7 Chapter Review - Additional Problems - Page 490: 18
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