An elementary matrix is a matrix that can be transform into an identity matrix with a single elementary row operation. In other word, doing one step of elementary row operation in Gaussian elimination is the same as multiplying an elementary matrix.

Example

The following elementary matrix

\left(\begin{array}{llll} 1 & 0 & 0 \ 2 & 1 & 0 \ 0 & 0 & 1 \end{array}\right)