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sorry that I am asking too many questions, I am preparing for an exam...

I have a matrix,

0 1 0

0 0 0

0 0 1

and I need to say if it has a diagonal form (I mean, if there are P and D such that D=P^-1*D*P)

I found that the eigenvalues are 0 and 1. I also know that if I use 0, I get the system

0 1 0 0

0 0 0 0

0 0 0 0

(after Gaussian process)

What can I say about the eigenvectors, do they exist ? the eigenvalue 0 had a dimension of 2. so I need 2 eigenvectors in order to say that P and D exist...