Q. If $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}\$and $\left| A^{3} \right| = 125,\$then the value of $\alpha$is
A) $\pm 1$
B) $\pm 2$
C) $\pm 3$
D) $\pm 5$
Explanation
(c)
$\because\ \ \left| A^{3} \right| = |{A|}^{3} = 125$
$\Rightarrow \begin{bmatrix}
\alpha & 2 \\
2 & \alpha
\end{bmatrix} = 5$
$\Rightarrow \alpha^{2} - 4 = 5\ \ \ \Rightarrow \ \ \alpha = \pm 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.