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

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

Answer:

From equation (1), we have:

Question 16:

If verify that A³ − 6A² + 9A − 4I = 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.