Help in Linear Algebra(Similar Matrices)

Hi guys,

I got in some trouble lately with a question in similar matrices. The question is:

If we have two 2*2 matrices, A and B, then find an invertible matrix P that makes A similar to B. All that without diagonalization. I tried to solve this by assuming an arbitrary matrix P using the relation below:

since, A=(P^-1)BP

then, BP = AP

The matrices A and B are as follows:

A=[ 3 2 ]

[-1 0 ]

B=[-1 2]

[ 0 1]

P = [ a b]

[ c d]

Thanks guys I really would like a hand in this. I would appreciate it a lot.