Let A= [ ccc 2 & 1 & 0 1 & 2 & -1 0 & -1 & 2 ]. If |adj(adj(adj 2… - Vidyadip

MCQ

Let $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$. If $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A))|=(16)^{ n }$, then $n$ is equal to

✓
$10$
B
$9$
C
$12$
D
$8$

✓

Answer

Correct option: A.

$10$

a
$| A |=2[3]-1[2]=4$

$\therefore|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A ))|$

$=|2 A |^{( n -1)^3} \Rightarrow|2 A |^8=16^n$

$\Rightarrow\left(2^3|A|\right)^8=16^n$

$\Rightarrow\left(2^3 \times 2^2\right)^8=16^n$

$=2^{40}=16^n$

$=16^{10}=16^n \Rightarrow n=10$

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