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Q4.    If A and B are symmetric matrices, prove that AB - BA is a skew symmetric matrix.

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  If A, B are symmetric matrices then 

                                                 A'=A       and      B' = B

we have,             \left ( AB-BA \right )'=\left ( AB \right )'-\left ( BA \right )'=B'A'-A'B'


                                                                                             = -(AB-BA)

                       Hence, we have  (AB-BA) = -(AB-BA)'

Thus,( AB-BA)' is skew symmetric.

Posted by

seema garhwal

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