Q18 of 98 Page 314

If A and B are symmetric matrices of the same order then (AB – BA) is always

Given A and B are symmetric matrices


A’ = A --- 1


B’ = B ---- 2


Now (AB – BA)’ = (AB)’ – (BA)’


=B’A’ – A’B’


[’ = B’A’ ]


= BA – AB [Using 1 and 2]


(AB – BA)’ = - (AB - BA)


AB-BA is a skew symmetric matrix.

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