`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`, t

Question

`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`, t

`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. symmetric
B. skew symmetric
C. `I-XY`
D. `-YX`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

5 views Answered 2023-02-05 15:29