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Misc. 4 - Chapter 3 Class 12 Matrices (Term 1)

Last updated at May 29, 2018 by

Misc 4 - If A and B are symmetric matrices, prove AB - BA is - Miscellaneous

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Misc. 4 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) ∴ (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. Hence proved

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