I have a question regarding two matrices. Are the following matrices similar and if so find a third matrix P such that:

A =

B =

As far as I can tell they are similar because they have the same eigenvalues: 1, 2, 3. If I plug in 1 for

I get:

This row reduces to:

Doesn't that have the zero solution? My understanding of this topic regarding diagonalization isn't the best. Thanks for any help...I realize I have two more eigenvalues to find eigenvectors for.