Example 14 If A = [■8(1&[email protected]&−1)] and B = [■8(0&[email protected]&0)] , find AB and BA. Prove that AB ≠ BA AB = [■8(1&[email protected]&−1)] [■8(0&[email protected]&0)] = [■8(1(0)+0 (1)&1(1)+0 (0)@0(0)+(−1)(1)&0(1)+(−1) (0))] = [■8(0+0&1+0`@0−1&0+0)] = [■8(0&1@−1&0)] BA = [■8(0&[email protected]&0)][■8(1&[email protected]&−1)] = [■8(0(1)+1(0)&0(0)+1(−1)@1(1)+0 (0)&1(0)+0 (−1))] = [■8(0+0&0−[email protected]+1&0+0)] = [■8(0&−[email protected]&0)] ≠ AB Hence AB ≠ BA Hence proved

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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.

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