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For ngeq3, A^n=A^(n-2)+A^2-1,where A=[[1...

For `ngeq3, A^n=A^(n-2)+A^2-1`,where `A=[[1, 0, 0], [1, 0, 1],[ 0, 1, 0]]` Determine `A^50` and `A^49`

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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 nge 3 and consider matrix underset(3xx3)(U) with its columns as U_(1), U_(2), U_(3), such that A^(50)U_(1)=[[1],[25],[25]],A^(50) U_(2)=[[0],[1],[0]]and A^(50) U_(3)[[0],[0],[1]] Trace of A^(50) equals