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(101)^(3)-(51)^(3)-(50)^(3)...

`(101)^(3)-(51)^(3)-(50)^(3)`

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Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ge 3 . And trace of a square matrix X is equal to the sum of elements in its proncipal diagonal. Further consider a matrix underset(3xx3)(uu) with its column as uu_(1), uu_(2), uu_(3) such that A^(50) uu_(1)=[(1),(25),(25)], A^(50) uu_(2)=[(0),(1),(0)], A^(50) uu_(3)=[(0),(0),(1)] Then answer the following question : The value of |uu| equals