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If F(x)=[("cos"x,-sin x,0),(sin x,cos x,...

If `F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)]` and `G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)]`, then `[F(x) G(y)]^(-1)` is equal to

A

`F(-x) G(-y)`

B

`G(-y) F(-x)`

C

`F(x^(-1))G(y^(-1))`

D

`G(y^(-1)) F(x^(-1))`

Text Solution

Verified by Experts

The correct Answer is:
B
We have.
`[F(x) G(y)]^(-1)=[G(y)]^(-1) [F(x)]^(-1)`
`=G(-y) F(-x)`
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