# 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 3:

Verify A (adj A) = (adj AA = I .  #### Question 4:

Verify A (adj A) = (adj AA = I .   #### 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 matrix show 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,   