Question

If $A=\left[\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right]$ and $|A^3|=125$, then $\alpha$ is equal to

• A. $\pm 3$
• B. $\pm 2$
• C. $\pm 5$
• D. 0

Answer 1

The correct option is A $\pm 3$

Given, $|A^3|=|A{|}^3=125$
$\Rightarrow |A|=5$

$\Rightarrow {\alpha }^2-4=5$

$\Rightarrow {\alpha }^2=9$
$\Rightarrow \alpha =\pm 3$