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Question

If A and B are symmetric matrices of the same order and X = AB + BA and Y = AB - BA, then (XY)T is equal to


A

XY

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B

YX

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C

-YX

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D

None of these

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Solution

The correct option is C

-YX


Given that A and B are symmetric.
AT=A, BT=B
X=AB+BAXT=(AB)T+(BA)T=BTAT+ATBT=BA+AB=X, ((AB)T=BTAT)Y=ABBAYT=(AB)T(BA)T=BTATATBT=BAAB=Y, ((AB)T=BTAT)Now (XY)T=YTXT=YX


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