Question

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

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm \sqrt{7}$
• D. $\pm \sqrt{5}$

Answer 1

The correct option is C

$\pm \sqrt{7}$

$|A^3|=({\alpha }^2-4{)}^3=27\Rightarrow {\alpha }^2-4=3\alpha =\pm \sqrt{7}$