# What can be said about the relationship between row equivalent and invertible matrices?

If $rref(A)$ = $I$ and $rref(B)$ = $I$, can we say that $A$ and $B$ are row equivalent?

My intuition says Yes, but I can't really prove it. If this is true, does that mean that all invertible matrices of the same dimensions are row equivalent?

(Assume that $A$, $B$ and $I$ are $n$ by $n$)

I couldn't find an answer to this, maybe it's there somewhere, but in that case I couldn't understand it.

Thanks.