# NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE

## JEE: NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE

The document NCERT Solutions, Determinants, Part -5, Class 12, Maths, Notes - JEE is a part of JEE category.
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Determinants

Exercise 4.5

Question 1: Find adjoint of each of the matrices.

Question 2: Find adjoint of each of the matrices.

Question 3:

Question 4:

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
. Verify that (AB)-1 = B-1A-1

From (1) and (2), we have:
(AB)−1 = B−1A−1
Hence, the given result is proved.

Question 13:
If
show that Hence find A-1.

Question 14:
For the matrix , find the numbers a and b such that A2 + aA + bI = O.

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.

Question 16:
If
verify that A3 − 6A2 + 9A − 4I = O and hence find A−1

From equation (1), we have:

Question 17:

Hence, the correct answer is B.

Question 18: If A is an invertible matrix of order 2, then det (A−1) is equal to

B. C. D.

Hence, the correct answer is B.

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