# If A is singular matrix, then adj(A) is

(a) Non-singular

(b) singular

(c) Symmetric

(d) Not defined

Answer

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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.

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.

Last updated date: 03rd Oct 2023

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