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A,B,C are three matrices of the same ord...

`A,B,C` are three matrices of the same order such that any two are symmetric and the `3^(rd)` one is skew symmetric. If `X=ABC+CBA` and `Y=ABC-CBA`, then `(XY)^(T)` is

A

A. symmetric

B

B. skew symmetric

C

C. `I-XY`

D

D. `-YX`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `(XY)^(T)=Y^(T)X^(T)`
`Y^(T)=(ABC-CBA)^(T)`
`=C^(T)B^(T)A^(T)-A^(T)B^(T)C^(T)`
`=-CBA+ABC=Y`
`X^(T)=(ABC+CBA)^(T)`
`=C^(T)B^(T)A^(T)+A^(T)B^(T)C^(T)`
`=-CBA-ABC=-X`
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