Question

If A = $\left[\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right]$ and $|A^3|$ = 27, then $\alpha$ =

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$|A{|}^3=27\Rightarrow |A|=3\Rightarrow \left|\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right|=3\Rightarrow \alpha =\pm \sqrt{7}$