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.(n_{1} , n_{2} , n_{3}) where n_{1} , n_{2} , n_{3} are three values of n satisfying the equation det.(P - nI) = 0, n_{1}< n_{2}< n_{3} .

[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}