Question

If $A$ is singular matrix, then $\text{adj}A$ is

• A. Singular
• B. Non-singular
• C. Symmetric
• D. Not defined

Answer 1

Answer: (A)

Singular

Given $\to A$ is singular matrix

$AAdjA=A.I$

$|A.AdjA|={\left|A\right|}^n$

$\left|A\right|.\left|AdjA\right|=\left|A^n\right|$

A is singular

$\Rightarrow \left|A\right|=0$

$\Rightarrow \left|AdjA\right|=0$

Option A