If A is a non-singular matrix of order 3,

Given:

$A$ is a non-singular matrix of order 3

As we know,

$\operatorname{adj}(\operatorname{adj} A)=|A|^{n-2} A$, where $n$ is the order of $A$

$\Rightarrow \operatorname{adj}(\operatorname{adj} A)=|A|^{3-2} A \quad(\because$ Order of $A$ is 3$)$

$\Rightarrow \operatorname{adj}(\operatorname{adj} A)=|A|^{1} A$

$\Rightarrow \operatorname{adj}(\operatorname{adj} A)=|A| A$

Hence, $\operatorname{adj}(\operatorname{adj} A)$ is equal to $\mid \underline{A \mid} \underline{A}$.