If \( A=\left[\begin{array}{rrr}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{...
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If \( A=\left[\begin{array}{rrr}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right] \) and \( \left|A^{2}\right|=25 \), find the value(s) of \( \alpha \)
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