MCQ
If $A=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right]$ and $\left|\mathrm{A}^3\right|=125$, then $\alpha=$
- ✓±3
- B±2
- C±5
- D$0$
Hint:
$\begin{aligned} & \left|A^3\right|=125 \\ & |A|^3=53 \ldots \ldots\left[\because\left|A^n\right|=|A|^n, n \in N\right]\end{aligned}$
∴ |A| = 5
$\left|\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right|=5$
$\begin{aligned} & a^2-4=5 \\ & \alpha^2=9\end{aligned}$
∴ α = ± 3
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