If for the matrix $A = \begin{bmatrix} \alpha & -2 \\ -2 & \alpha \end{bmatrix}, |A^3| = 125$, then the value of $\alpha$ is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\pm 3$ ##
Given, $A = \begin{bmatrix} \alpha & -2 \\ -2 & \alpha \end{bmatrix}$
$⇒|A| = \alpha^2 - 4$ ...(i)
Also, given $|A^3| = 125$
$⇒|A|^3 = 125$
$⇒|A| = 5$
From eq. (i): $\alpha^2 - 4 = 5$
$⇒ \alpha^2 = 9$
$⇒ \alpha = \pm 3$