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Ex 3.3, 11 - If A, B are symmetric matrices, then AB - BA

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Ex 3.3, 11 If A, B are symmetric matrices of same order, then AB − BA is a A. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix A and B are symmetric matrices, ∴ A’ = A and B’ = B Consider (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA − AB = − (AB – BA) ∴ (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. ∴ Correct answer is A. [(A – B)’ = A’ – B’] [(AB)’ = B’A’] [By (1)]

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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.