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If f(x)=[(cosx,-sinx,0),(sinx ,cosx,0),(...

If `f(x)=[(cosx,-sinx,0),(sinx ,cosx,0),(0,0,1)] and g(y)=[(cosy,0,siny),(0,1,0),(-siny,0,cosy)],` 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)`

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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