Check sibling questions

Example 13 - Find AB, BA. Show that AB not = BA. A = [1 -2 3

Example 13 - Chapter 3 Class 12 Matrices - Part 2

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 13 If A = [■8(1&−2&3@−4&2&5)] and B = [■8(2&3@4&5@2&1)] then find AB, BA . Show that AB ≠ BA AB =[■8(1&−2&3@−4&2&5)]_(2 × 3 ) [■8(2&3@4&5@2&1)]_(3 × 2) = [■8(1 × 2+(−2) × 4+3 × 2&1 × 3+(−2) × 5+3 × 1@−4 × 2+2 × 4+5 × 2&−4 × 3+2 × 5+5 × 1)]_(2 × 2 ) = [■8(2−8+6&3−10+3@−8+8+10&−12+10+5)] = [■8(0&−4@10&3)] . BA = [■8(2&3@4&5@2&1)]_(3 × 2) [■8(1&−2&3@−4&2&5)]_(2 × 3) = [■8(2 × 1+3 × (−4)&2 × (−2)+3 × 2&2 × 3+3 × 5@4 × 1+5 × (−4)&4 × (−2)+5 × 2&4 × 3+5 × 5@2 × 1+1 × (−4)&2 × (−2)+1 × 2&2 × 3+1 × 5)]_(3 × 3 ) = [■8(2−12&−4+6&6+15@4−20&−8+10&12+25@2−4&−4+2&6+5)] = [■8(−10&2&21@−16&2&37@−2&−2&11)] ≠ AB Hence AB ≠ BA

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.