Matrices and Determinants 2 Question 14
16. If $A=\begin{vmatrix}\alpha & 2 \\ 2 & \alpha\end{vmatrix}$ and $\left|A^{3}\right|=125$, then the value of $\alpha$ is
(a) $\pm 1$
(b) $\pm 2$
(c) $\pm 3$
(d) $\pm 5$
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Answer:
Correct Answer: 16. (c)
Solution:
- We know, $\left|A^{n}\right|=|A|^{n}$
Since,
$ \left|A^{3}\right|=125 \Rightarrow|A|^{3}=125 $
$\Rightarrow \quad \begin{vmatrix}\alpha & 2 \\ 2 & \alpha\end{vmatrix}=5 \Rightarrow \alpha^{2}-4=5 \Rightarrow \alpha= \pm 3$
