# GATE Mechanical 2021 Set 2 | Question: 1

Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $\text{p}$. Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1,0,1 \right \}$. Based on the given information, the eigen value of $A^{2}$ is:

1. $\alpha$
2. $\alpha ^{2}$
3. $\surd{\alpha }$
4. $\alpha ^{4}$

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