## NCERT Solutions for Class 12 Maths Chapter 4 – Determinants Ex 4.5

#### Page No 131:

#### Question 1:

Find adjoint of each of the matrices.

#### Answer:

#### Question 2:

Find adjoint of each of the matrices.

#### Answer:

#### Question 3:

Verify

*A*(*adj A*) = (*adj A*)*A*=*I*.#### Answer:

#### Question 4:

Verify

*A*(*adj A*) = (*adj A*)*A*=*I*.#### Answer:

#### Page No 132:

#### Question 5:

Find the inverse of each of the matrices (if it exists).

#### Answer:

#### Question 6:

Find the inverse of each of the matrices (if it exists).

#### Answer:

#### Question 7:

Find the inverse of each of the matrices (if it exists).

#### Answer:

#### Question 8:

Find the inverse of each of the matrices (if it exists).

#### Answer:

#### Question 9:

Find the inverse of each of the matrices (if it exists).

#### Answer:

#### Question 10:

Find the inverse of each of the matrices (if it exists).

.

#### Answer:

#### Question 11:

Find the inverse of each of the matrices (if it exists).

#### Answer:

#### Question 12:

Let and. Verify that

#### Answer:

From (1) and (2), we have:

(

*AB*)^{−1}=*B*^{−1}*A*^{−1}
Hence, the given result is proved.

#### Question 13:

If, show that. Hence find.

#### Answer:

#### Question 14:

For the matrix, find the numbers

*a*and*b*such that*A*^{2}+*aA*+*bI*=*O*.#### Answer:

We have:

Comparing the corresponding elements of the two matrices, we have:

Hence, −4 and 1 are the required values of

*a*and*b*respectively.#### Question 15:

For the matrixshow that

*A*^{3}− 6*A*^{2}+ 5*A*+ 11*I*= O. Hence, find*A*^{−1.}#### Answer:

From equation (1), we have:

#### Question 16:

If verify that

*A*^{3}− 6*A*^{2}+ 9*A*− 4*I*=*O*and hence find*A*^{−1}#### Answer:

From equation (1), we have:

#### Question 17:

Let

*A*be a nonsingular square matrix of order 3 × 3. Then is equal to**A.**

**B.**

**C.**

**D.**

#### Answer:

**Answer: B**

We know that,

Hence, the correct answer is B.

#### Question 18:

If

*A*is an invertible matrix of order 2, then det (*A*^{−1}) is equal to**A.**det (

*A*)

**B.**

**C.**1

**D.**0

#### Answer:

Since

*A*is an invertible matrix,
Hence, the correct answer is B.

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