Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \ 0 & \alpha & 5 \alpha \ 0 & 0 & 5\end{array} ight]$. If $\left|A^2 ight|=25$, then $|\alpha|$ equals

Question

Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \ 0 & \alpha & 5 \alpha \ 0 & 0 & 5\end{array}ight]$. If $\left|A^2ight|=25$, then $|\alpha|$ equals

Aicharya · Accepted Answer

$\mathrm{A}^2=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \ 0 & \alpha & 5 \alpha \ 0 & 0 & 5\end{array}ight]\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \ 0 & \alpha & 5 \alpha \ 0 & 0 & 5\end{array}ight]$ $\mathrm{A}^2=\left[\begin{array}{ccc}25 & 25 \alpha+5 \alpha^2 & 5 \alpha+25 \alpha^2+5 \alpha \ 0 & \alpha^2 & 5 \alpha^2+25 \alpha \ 0 & 0 & 25\end{array}ight]$ $625 \alpha^2=25$ $\Rightarrow|\alpha|=\frac{1}{5}$.

Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 &…

Solution