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There exists a matrix Q such that PQP T = N, where P = [(1,2,0)(2,1,0)(0,0,1)] .

Given N is a diagonal matrix of form N = diag.(n1 , n2 , n3) where n1 , n2 , n3 are three values of n satisfying the equation det.(P - nI) = 0, n1< n2< n3 .

[Note : I is an identity matrix of order 3×3]

The trace of matrix P 2012 is equal to

 (A) 3 2011

 (B) 3 2012

(C) 3 2012 + 2

 (D) 3 2011

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Correct option  (C) 32012 + 2


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