Elementary Matrices

An elementary matrix, $E$, is one that differs by $I_n$ by one row operation Note:

1. Every $E$ is invertible
2. Every $E$ is square

For example, $\left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 0& 0& 1\end{array}\right]$ is an elementary matrix as it differs from $I_3$ by one row operation ($R_2=R_2-2R_1$)

What Do They Represent

Each elementary matrix represents a row operation.