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If A=[(costheta, -sin theta ),(sin theta...

If `A=[(costheta, -sin theta ),(sin theta, cos theta) ]` , then the matrix `A^(-50)` when `theta=pi/12`, is equal to :

A

`(((sqrt(3))/(2),(1)/(2)),(-(1)/(2),(sqrt(3))/(2)))`

B

`(((1)/(2),(sqrt(3))/(2)),(-(sqrt(3))/(2),(1)/(2)))`

C

`(((1)/(2),-(sqrt(3))/(2)),((sqrt(3))/(2),(1)/(2)))`

D

`(((sqrt(3))/(2),-(1)/(2)),((1)/(2),(sqrt(3))/(2)))`

Text Solution

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The correct Answer is:
A
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