If A= & 2 2 & and |A^3|=125, then is equal to: - Vidyadip

MCQ

If $\text{A}=\begin{bmatrix}\alpha &\text{amp; 2} \\2 &\text{amp; }\alpha \end{bmatrix}$and $ |\text{A}^3|=125,$ then $\alpha$ is equal to:

✓
$\pm 3$
B
$\pm 2$
C
$\pm 5$
D
$0$

✓

Answer

Correct option: A.

$\pm 3$

Given, $ |\text{A}^3| =|\text{A}|^3 = 125$

$\Rightarrow|\text{A}|=5\Rightarrow\alpha^2-4=5\Rightarrow\alpha^2=9$

$\Rightarrow \alpha=\pm 3$

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