Solve this

Given:

$A=\operatorname{diag}(1,2,3)$

$\Rightarrow|A|=1 \times 2 \times 3=6$

As we know,

$|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(n-1)^{2}}$, where $n$ is the order of $A$

$\Rightarrow|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(3-1)^{2}} \quad(\because$ Order of $A$ is 3$)$

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

$\Rightarrow|\operatorname{adj}(\operatorname{adj} A)|=|A|^{4}$

$\Rightarrow|\operatorname{adj}(\operatorname{adj} A)|=6^{4} \quad(\because|A|=6)$

$\Rightarrow|\operatorname{adj}(\operatorname{adj} A)|=1296$

Hence, $|\operatorname{adj}(\operatorname{adj} A)|=\underline{1296}$.