OK. Forget the top.

How could I show that the following two matrices are similar without mentioning eigenvalues?

2 1 -1 0

0 4 -2 0

0 3 -1 0

0 3 -2 1

and

2 1 -2 1

0 4 -4 2

0 3 -4 3

0 3 -5 4

They are similar, but what is the matrix P such that A=inv(P)*B*P?