If A is an invertible matrix of order 3

Given:

$A$ is an invertible matrix of order 3

$|A|=3$

As we know,

$|\operatorname{adj} A|=|A|^{n-1}$, where $n$ is the order of $A$

$\Rightarrow|\operatorname{adj} A|=|A|^{3-1} \quad(\because$ Order of $A$ is 3$)$

$\Rightarrow|\operatorname{adj} A|=|A|^{2}$

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

$\Rightarrow|\operatorname{adj} A|=9$

Hence, $|\operatorname{adj} A|=\underline{9}$.