Suppose that $A$ is an $m\times n$ matrix, and $B$ is a matrix of the same size that is obtained from $A$ by a single row operation (Definition RO). Then there is an elementary matrix of size $m$ that will convert $A$ to $B$ via matrix multiplication on the left. More precisely,

1. If the row operation swaps rows $i$ and $j$, then $B=\elemswap{i}{j}A$.
2. If the row operation multiplies row $i$ by $\alpha$, then $B=\elemmult{\alpha}{i}A$.
3. If the row operation multiplies row $i$ by $\alpha$ and adds the result to row $j$, then $B=\elemadd{\alpha}{i}{j}A$.