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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:

- $\alpha$
- $\alpha ^{2}$
- $\surd{\alpha }$
- $\alpha ^{4}$

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Here the Equation is given as

Ap=(α^2)p

Here p is a non zero vector

A is the matrix

We are linearly transforming(Multiplying a Matrix with a Vector is Linear Transformation) a Non zero Vector By a Matrix A

The Changing is Same as multiplying that Vector with a Scalar

So, this is Straight enough that (α^2) is eigen value of A

And We know if k is a eigen value of A

Then K^2 will be the eigen value of A^2

Similarly Here Also (α^4) would be the eigen value of A^2