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If A(alpha, beta)=[("cos" alpha,sin alph...

If `A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))]`, then `A(alpha, beta)^(-1)` is equal to

A

`A(-alpha, -beta)`

B

`A(-alpha, beta)`

C

`A(alpha, -beta)`

D

`A(alpha, beta)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`A(alpha, beta)^(-1)=1/e^(beta) [(e^(beta) cos alpha,-e^(beta) sin alpha,0),(e^(beta) sin alpha,e^(beta) cos alpha,0),(0,0,1)]`
`=A(-alpha, -beta)`
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