similar and invertible matrices

[jazzman]

Hey all!
I have to prove or disprove the following statement:
"If matrices A and B are similar and row-equivalent then A=B".

I am trying to prove it since I didn't manage to disprove it yet...
I now that if A and B are similar then there exists a matrix P so that: $\displaystyle A=P^{-1}BP$.
I also know that if A and B are row-equivalent then: $\displaystyle A=E_1\cdot{E_2}\cdots{E_n}{B}$ when $\displaystyle E_i$ are elementary matrices.
I am not sure how to continue from here...

Can someone please tell me if this sentence is true and if it is, how should I continue?