I'm a little confused about similar matrices.

Are the the following matrices similar?

Now I know that similar matrices share a variety of properties....some of which I've already calculated.

Rank = 2, Determinant = 0, Trace = 1, Char. Polynomial =

Rank = 3, Determinant = 2, Trace = 2, Char. Polynomial =

From this I would say that these two aren't similar, however, I have read other posts on this forum that make me think that the above properties aren't enough to safely conclude that the are or are not similar.

I am aware that if 2 matrices, A and B, are similar then there is a matrix P such that

.

How then, do I calculate P?

Thanks in advance for any help