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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.