$\begin{bmatrix} 1 & 0 & 0 \\ \hline 2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix}$ is called an elementary row-addition matrix as:

$$\begin{bmatrix} 1 & 0 & 0 \\ \hline 2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix} \underbrace{ \begin{bmatrix} b_1 \\ \hline b_2 \\ \hline b_3 \end{bmatrix}}_{Matrix B} = \begin{bmatrix} b_1 \\ \hline 2 b_1 + b_2 \\ \hline b_3 \end{bmatrix}$$

Property

Invertible

A row-addition matrix is Linear Algebra - Matrix.

$\begin{bmatrix} 1 & 0 & 0 \\ \hline 2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix}$ and $\begin{bmatrix} 1 & 0 & 0 \\ \hline -2 & 1 & 0 \\ \hline 0 & 0 & 1 \end{bmatrix}$ are Linear Algebra - Matrix.