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Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ 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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