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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

`[{:(,(1)/(2),-(sqrt3)/(2)),(,(sqrt3)/(2),(1)/(2)):}]`

B

`[{:(,(sqrt3)/(2),(1)/(2)),(,-(1)/(2),(sqrt3)/(2)):}]`

C

`[{:(,(sqrt3)/(2),-(1)/(2)),(,(1)/(2),(sqrt3)/(2)):}]`

D

`[{:(,(1)/(2),(sqrt3)/(2)),(,-(sqrt3)/(2),(1)/(2)):}]`

Text Solution

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The correct Answer is:
B
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