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Question

Let A and B be two symmetric matrices of same order. If X=AB+BA and Y=ABBA, then (XY)T is equal to

A
YX
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B
XY
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C
XY
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D
YX
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Solution

The correct option is D YX
A and B are two symmetric matrices.
AT=A and BT=B
(XY)T=YTXT

XT=(AB+BA)T
=(AB)T+(BA)T
=BTAT+ATBT
=BA+AB=X
Similarly, YT=(ABBA)T=BAAB=Y

Hence, (XY)T=YX

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