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If A and B are symmetric matrices of th...

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` (B) `YX` (C) `-YX` (D) non of these

A

`XY`

B

`YX`

C

`-YX`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given that
`X=AB+BAimplies X=X^(T)" "( :' A=A^(T) and B=B^(T))`
and `Y=AB-BA`
`implies Y=-Y^(T)`
Now, `(XY)^(T)=Y^(T)X^(T)=-YX`.
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