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

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

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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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