Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$|\text{adj(adj}A)|=|A{|}^{(n-1{)}^2}=|A{|}^9$
$\Rightarrow (n-1{)}^2=9n-1=3\Rightarrow n=4$