If $A$ is a square matrix of order $n,$ such that $| adj(adj A) | = | A |^{9},$ then $n$ is

1

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Solution

The correct option is D $4$
$| adj(adj A) | = | A |^{(n - 1)^{2}} = | A |^{9}$
$\Rightarrow (n - 1)^{2} = 9 n - 1 = 3 \Rightarrow n = 4$

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