If $A$ is a square matrix of order $n$ such that |adj(adjA)|$= |A|^{9}$then the value of $n$ can be

Question

Dr. Abubacker · Accepted Answer

(a)
We know that in a square matrix of order $n$,
$|adj\ A| = |A|^{n - 1}$
$\Rightarrow \left| adj(adj\ A) \right| = |adj\ A|^{n - 1} = |A|^{(n - 1)^{2}}$
$\Rightarrow n^{2} - 2n - 8 = 0$
$\Rightarrow n = 4\$as$\ n = - 2\$ is not possible

Q. If $A$ is a square matrix of order $n$ such that |adj(adjA)|$= |A|^{9}$then the value of $n$ can be

Explanation

Reviewed by Dr. Abubacker

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