# Example 25 - Chapter 4 Class 12 Determinants

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 25 If A = 2 3 1 4 and B = 1 2 1 3 , then verify that (AB)-1 = B-1 A-1 Taking L .H.S (AB) 1 First calculating AB AB = 2 3 1 4 1 2 1 3 = 2 1 +3( 1) 2 2 +3(3) 1 1 +( 4)( 1) 1 2 + 4 3 = 2 3 4+9 1+4 2 12 = 1 5 5 14 Now, (AB)-1 = 1 |AB| adj (AB) exists if |AB| 0 |AB| = 1 5 5 14 = (-1)(-14) 5(5) = 14 25 = 11 Since |AB| 0 (AB)-1 exists AB = 1 5 5 14 adj (AB) = 1 5 5 14 = 14 5 5 1 Now, (AB) 1 = 1 |AB| adj (AB) Putting values = 1 11 14 5 5 1 = 1 11 14 5 5 1 Taking R.H.S B-1A-1 First Calculating B 1 B = 1 2 1 3 B = 1 |B| adj (B) exists if |B| 0 |B| = 1 2 1 3 = 3 2 = 1 Since |B| 0 , B-1 exist B = 1 2 1 3 adj (B) = 1 2 1 3 = 3 2 1 1 Now, (B) 1 = 1 |B| adj (B) Putting values = 1 1 3 2 1 1 = 3 2 1 1 Finding A-1 A-1 = 1 |A| adj (A) exists if |A| 0 |A| = 2 3 1 4 = 2 ( 4) 1( 3) = 8 3 = 11 Since |A| 0 , A 1 exists A = 2 3 1 4 adj (A) = 2 3 1 4 = 4 3 1 2 Now, A-1 = 1 |A| adj (A) = 1 11 4 3 1 2 = 1 11 4 3 1 2 Thus, B-1A-1 = 3 2 1 1 1 11 4 3 1 2 = 1 11 3 2 1 1 4 3 1 2 = 1 11 3 4 +2(1) 3 3 +2( 2) 1 4 +1(1) 1 3 +1( 2) = 1 11 12+2 9 4 4+1 3 2 = 1 11 14 5 5 1 = L.H.S L.H.S = R.H.S Hence proved

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14 Important

Example 15 Important

Example 16 Important

Example 17

Example 18 Important

Example 19

Example 20

Example 21

Example 22

Example 23

Example 24 Important

Example 25 You are here

Example 26 Important

Example 27

Example 28

Example 29

Example 30

Example 31

Example 32 Important

Example 33

Example 34 Important

Chapter 4 Class 12 Determinants

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.