If A = [ * 20 c &2 2& ] and | A^3 |=125, then = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}\alpha &2\\2&\alpha \end{array}} \right]$ and $|{A^3}|$=125, then $\alpha = $

✓
$ \pm $ $3$
B
$ \pm $ $2$
C
$ \pm $ $5$
D
$0$

✓

Answer

Correct option: A.

$ \pm $ $3$

a
(a) $|{A^3}| = 125$; $|A{|^3} = 125 = {5^3}$

$ \Rightarrow $ $|A| = 5$ $ \Rightarrow $ ${\alpha ^2} - 4 = 5 \Rightarrow \alpha = \pm 3$.

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