I am trying to find the eigenvalues . They are 0 and 2 but i keep on just getting 0.

its a4X4 matrix.
[ 1 1 0 0
1 1 0 0
0 0 0 0
0 0 0 0]

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