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  4. If A, B are symmetric matrices of the same order then AB - BA is a

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Q. If A, B are symmetric matrices of the same order then AB - BA is a

Matrices

Solution:

A and B are symmetric matrices $\Rightarrow \, A' = A$
$\Rightarrow \, B' = B $
Now $(AB - BA)' = (AB)' - (BA)'$
$= B'A' - A'B' = BA - AB$
$\because \, B' = B, A' = A = - (AB - BA)$
$ \Rightarrow \, (AB - BA) $ is a skew symmetric matrix.