Matrices And Determinants Ques 37

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) $\pm 5$

Show Answer

Answer:

Correct Answer: 37.(c)

Solution:

Formula:

PROPERTIES OF DETERMINANTS:

  1. We know, $\left|A^{n}\right|=|A|^{n}$

Since,

$ \left|A^{3}\right|=125 \Rightarrow|A|^{3}=125 $

$\Rightarrow \quad \begin{vmatrix}\alpha & 2 \\ 2 & \alpha\end{vmatrix}=5 \Rightarrow \alpha^{2}-4=5 \Rightarrow \alpha= \pm 3$

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