Q45 / 160 · AP EAMCET 2022 (04 Jul Shift 1) · Mathematics

If $A = [\begin{matrix} α^{2} & 5 \\ 5 & - α \end{matrix}]$ and $det (A^{10}) = 1024$ , then $α =$

A
$- 2$
B
$- 1$
Correct answer
C
$- 3$
D
$0$

Solution

$A = [\begin{matrix} α^{2} & 5 \\ 5 & - α \end{matrix}]$
$|A| = - α^{3} - 25$
Now $|A^{10}| = {|A|}^{10} = 2^{10}$
$\Rightarrow |A| = 2$
i.e. $- α^{3} - 25 = 2 \Rightarrow α = - 3$

Hence, the correct answer is option: 'C'.

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