You have the eigenvalues right, but what is this matrix associated with the eigenvalue? I've never heard of it. Anyway, to get the eigenvectors:

:

Let the eigenvector be

So:

Thus or a = 0, and which says that , leaving b undetermined. So the eigenvector for is of the form

where b is undetermined.

You can use the same method to get the eigenvector for .

-Dan