If A is a singular matrix, then adj A is

(b) singular

$A$ is singular, so $|A|=0$.

By definition, we have

$A \operatorname{adj}(A)=O$

$\Rightarrow \mid A$ adj $(A)|=| O \mid$

$\Rightarrow|A||\operatorname{adj}(A)|=0$

$\Rightarrow|\operatorname{adj}(A)|=0$

Hence, adj $(A)$ is singular.