Adjoint of a matrix Practice Questions - NDA Mathematics Question Bank

Question 1 of 5 NDA MCQ

Let A be a non-singular matrix and B = adjA.

Which of the following statements is/are correct?

(1) AB = BA

(2) AB is a scalar matrix

(3) AB can be a null matrix

Select the correct answer using the code given below:

Detailed Explanation

Explanation:

We know that for a square matrix A of order n,

A(adj A) = (adj A)A = |A|I given that B = adj A

∴

AB = BA

So, statement 1 is correct.

AB = |A|I is scalar matrix but not null matrix

So, statement 2 is correct and statement 3 is not

correct.

Hints:

•

Use A(adj A) = (adj A)A = |A|I

•

If adj = constant for i = j then matrix A is

called scalar matrix.

Question 2 of 5 NDA MCQ

Select the correct answer using the code given

below

Detailed Explanation

Question 3 of 5 NDA MCQ

Consider the following statements in respect of two non-singular matrices A and B of the same order n:

1. adj(AB) = (adj A)(adj B)

2. adj(AB) = adj(BA)

3. (AB)adj(AB) – |AB|In is a null matrix of order n

How many of the above statements are correct?

Detailed Explanation

Question 4 of 5 NDA MCQ

If A = , then which of the following statements is/are correct?

1. A^–1 = adj A

2. A is skew-symmetric matrix

3. A^–1 = A^T

Select the correct answer using the code given below:

Detailed Explanation

Question 5 of 5 NDA MCQ

For the following two (02) items:

Let A

What is [adj A]^–1 equal to?

Detailed Explanation

Adjoint of a matrix