Misc 1 - Chapter 3 Class 12 Matrices

Last updated at Dec. 16, 2024 by

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Misc 1 If A and B are symmetric matrices, prove that AB − BA is a skew symmetric matrix. Given A and B are symmetric matrices ∴ A’ = A and B’ = B Now, (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA – AB = − (AB – BA) Since (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo