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If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]],...

If `P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]]` and `Q=PAP^T` and `X=P^TQ^(2005)P`, then `X` equal to:
A. `[[1,2005],[0,1]]`
B. `[[4+2005sqrt3,6015],[2005,4-2005sqrt3]]`
C. `1/4 [[2+sqrt3,1],[-1,2-sqrt3]]`
D. `1/4 [[2005,2-sqrt3],[2+sqrt3,2005]]`

A

`[(1,2005),(0,1)]`

B

`[(sqrt(3)//2,2005),(1,0)]`

C

`[(1,2005),(sqrt(3)//2,1)]`

D

`[(1,sqrt(3)//2),(0,2005)]`

Text Solution

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The correct Answer is:
A
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