# NCERT solution class 12 chapter 3 Matrices exercise 3.4 mathematics part 1

## EXERCISE 3.4

#### Question 1:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 2:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 3:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 4:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 5:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 6:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 7:

Find the inverse of each of the matrices, if it exists.

We know that A = AI

#### Question 8:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 9:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 10:

Find the inverse of each of the matrices, if it exists.

We know that A = AI

#### Question 11:

Find the inverse of each of the matrices, if it exists.

We know that A = AI

#### Question 12:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Now, in the above equation, we can see all the zeros in the second row of the matrix on the L.H.S.

Therefore, A−1 does not exist.

#### Question 13:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 14:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Applying, we have:

Now, in the above equation, we can see all the zeros in the first row of the matrix on the L.H.S.

Therefore, A−1 does not exist.

#### Question 15:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

#### Question 16:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Applying R2 → R2 + 3R1 and R3 → R3 − 2R1, we have:

#### Question 17:

Find the inverse of each of the matrices, if it exists.

We know that A = IA

Applying, we have:

#### Question 18:

Matrices A and B will be inverse of each other only if

A. AB = BA

C. AB = 0, BA = I

B. AB = BA = 0

D. AB = BA = I