Question

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

• A. 4
• B. 2
• C. either 4 or 2
• D. None of these

Answer 1

The correct option is A

4

We know that for a square matrix of order n, |adj A| $=|A{|}^{n-1}$
$\Rightarrow |adj\left(adjA\right)|=|adjA{|}^{n-1}=|A{|}^{(n-1{)}^2}=|A{|}^9\Rightarrow (n-1{)}^2=9\Rightarrow n^2-2n-8=0$
$\Rightarrow$ n = 4 as n =-2 is not possible.