If A and B are symmetric matrices, prove that AB$-$BA is a skew symmetric matrix.
If A and B are symmetric matrices, prove that AB$-$BA is a skew symmetric matrix.
Official Solution
VVidaara Team
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.:
Given. : A and B are symmetric matrices, therefore $A' = A, B' = B.$
To prove :(AB$- BA)'= -$(AB$-$BA)
Proof : $(AB$ - $BA)'$=$(AB)'$ -
$(BA)$=$B'A'$ - $A'B'=BA$ - $AB =$ -
$(AB$ - $BA)$
So, AB$-$BA is a skew-symmetric matrix.
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