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given your matrix A, we need to solve
det(nI-A) = 0
so we need to solve
|n-1 -1 0 0|
|-1 n-1 0 0|
|0 0 n 0|
|0 0 0 n|
= 0
That is n^3(n-2) = 0
As you can see, n = 0,0,0,2