# NCERT solution class 12 chapter 4 Determinants exercise 4.5 mathematics part 1

## EXERCISE 4.5

#### Question 1:

Find adjoint of each of the matrices.

#### Question 2:

Find adjoint of each of the matrices.

#### Question 5:

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

#### Question 6:

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

#### Question 7:

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

#### Question 8:

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

#### Question 9:

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

#### Question 10:

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

.

#### Question 11:

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

#### Question 12:

Let and. Verify that

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

(AB)−1 = B−1A−1

Hence, the given result is proved.

#### Question 13:

If, show that. Hence find.

#### Question 14:

For the matrix, find the numbers a and b such that A2 + aA + bI O.

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 A3 − 6A2 + 5A + 11 I = O. Hence, find A−1.

From equation (1), we have:

#### Question 16:

If verify that A3 − 6A2 + 9A − 4I = O and hence find A−1

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.

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 (AB.  C. 1 D. 0

Since A is an invertible matrix,

Hence, the correct answer is B.

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