If A is a singular matrix, then A(adj A) is equal to

The correct answer is Option (2) → a null matrix

Given that matrix $A$ is singular.

This means:

$\text{det}(A) = 0$

Now, the identity:

$A \cdot \text{adj}(A) = \text{det}(A) \cdot I$

Substitute $\text{det}(A) = 0$:

$A \cdot \text{adj}(A) = 0 \cdot I = 0$

Therefore,

$A \cdot \text{adj}(A) = 0$