## EXERCISE 3.4

#### Page No 97:

#### Question 1:

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

#### Answer:

We know that *A* = *IA*

#### Question 2:

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

#### Answer:

We know that *A* = *IA*

#### Question 3:

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

#### Answer:

We know that *A* = *IA*

#### Question 4:

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

#### Answer:

We know that *A* = *IA*

#### Question 5:

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

#### Answer:

We know that *A* = *IA*

#### Question 6:

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

#### Answer:

We know that *A* = *IA*

#### Question 7:

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

#### Answer:

We know that *A* = *AI*

#### Question 8:

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

#### Answer:

We know that *A* = *IA*

#### Question 9:

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

#### Answer:

We know that *A* = *IA*

#### Question 10:

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

#### Answer:

We know that *A* = *AI*

#### Question 11:

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

#### Answer:

We know that *A* = *AI*

#### Question 12:

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

#### Answer:

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.

#### Answer:

We know that *A* = *IA*

#### Question 14:

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

#### Answer:

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.

#### Answer:

We know that *A* = *IA*

#### Question 16:

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

#### Answer:

We know that *A* = *IA*

Applying R_{2} → R_{2} + 3R_{1} and R_{3} → R_{3} − 2R_{1}, we have:

#### Question 17:

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

#### Answer:

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*

#### Answer:

**Answer: D**

We know that if *A* is a square matrix of order *m*, and if there exists another square matrix *B* of the same order *m*, such that *AB* = *BA* = *I*, then *B* is said to be the inverse of *A*. In this case, it is clear that *A* is the inverse of *B*.

Thus, matrices *A* and *B* will be inverses of each other only if *AB* = *BA* = *I*.