Question

If A is singular matrix, then adj(A) is
(a) Non-singular
(b) singular
(c) Symmetric
(d) Not defined

Answer 1

Hint: Apply property of matrix i.e. $adjA = \left| A \right| \cdot I$ where A is a singular matrix. From this property, we will get our answer.

Complete step-by-step answer:
Since A is singular matrix
Then $\left| A \right| = 0$
As we know that
$adjA = \left| A \right| \cdot I$
$\Rightarrow adjA = 0$
Hence adjA is a singular matrix
So option (a) is correct

NOTE: Whenever you come to this type of problem try to apply properties of the matrix to get the answer in a simple way and need to remember different types of matrix and their properties.