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  4. Let A and B be two symmetric matrices of same order. Then, the matrix AB-BA is

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Q. Let $ A $ and $ B $ be two symmetric matrices of same order. Then, the matrix $ AB-BA $ is

ManipalManipal 2009

Solution:

Given, $A=A ', B=B '$
Now, $(A B-B A) '=(A B)'-(B A) '$
$=B ' A '-A ' B '$
$=B A-A B$
$=-(A B-B A)$
$\therefore A B-B A$ is a skew-symmetric matrix.