Question

If $A=\left|\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right|and|A^3|=125$, then the value of $\alpha$ is

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 5$

Answer 1

The correct option is C $\pm 3$

We know, $|A^n|=|A{|}^n$
Since, $|A^3|=125\Rightarrow |A{|}^3=125$
$\Rightarrow \left|\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right|=5\Rightarrow {\alpha }^2-4=5\Rightarrow \alpha =\pm 3$