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Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $\left|A^2\right|=25$, then $|\alpha|$ equals
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$1 / 5$
$1 / 5$
$\mathrm{A}^2=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$
$\mathrm{A}^2=\left[\begin{array}{ccc}25 & 25 \alpha+5 \alpha^2 & 5 \alpha+25 \alpha^2+5 \alpha \\ 0 & \alpha^2 & 5 \alpha^2+25 \alpha \\ 0 & 0 & 25\end{array}\right]$
$625 \alpha^2=25$
$\Rightarrow|\alpha|=\frac{1}{5}$.
$\mathrm{A}^2=\left[\begin{array}{ccc}25 & 25 \alpha+5 \alpha^2 & 5 \alpha+25 \alpha^2+5 \alpha \\ 0 & \alpha^2 & 5 \alpha^2+25 \alpha \\ 0 & 0 & 25\end{array}\right]$
$625 \alpha^2=25$
$\Rightarrow|\alpha|=\frac{1}{5}$.
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