matrices - left multiplication by invertible matrix doesn't change reduced row echelon form

How to proof that for the matrices:

$A=\begin{pmatrix} 1 & 0 \\ a & 1 \end{pmatrix}$ and $B=\begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}$,
$X\in M_{23}(\mathbb R)$

$A(BX)$ has the same reduced row echelon form as $X$ ?

Of course I know: $A(BX) <=> (AB)X$, A is an elementary matrix and B is the product of an elementary matrix. I also know, that the reduced row echelon form is distinct. But how to show that ?