I am supposing that $E$ is the elementary matrix obtained from $I$ (the identity matrix), by adding $\mu$ times the $m$-th row to the $l$-th row for some $\mu \in \mathbb{R}$ and $1\leq l,m\leq n$ and $l\neq m$.

I need to prove that for any $n\times n$ the matrix $B=EA$ can be obtained from $A$ by applying the same row operations.

I think I need to start by stating $E=e\_{ik}$, so $e\_{ik}= \left\{
 \begin{array}{2 2}
 1 \quad \text{if} \space i=k & \quad \\ \mu \quad \text{if} \space i=l \space \text{and} \space k=m & \quad \\0 \quad \text{otherwise}
 \end{array} \right.$

But I'm not sure where to go from there. I'm not very good at matrices so a bit more in depth explanation would be appreciated.