An elementary matrix is one that is obtained by performing a single elementary row operation on identity matrix
The elementary matrix itself is produced by the same row operation on the identity matrix
$$ \begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ -4 & 0 & 1\end{bmatrix}\begin{bmatrix}x_1\\ x_2\\ x_3\end{bmatrix}= x_1\begin{bmatrix}1\\ 0\\ -4\end{bmatrix}+x_2\begin{bmatrix}0\\ 1\\ 0\end{bmatrix}+x_3\begin{bmatrix}0\\ 0\\ 1\end{bmatrix}= \begin{bmatrix}x_1\\ x_2\\ x_3 - 4x_1\end{bmatrix} $$
we can see that changing one element in the 3rd row , we are doing the operation $r_3 = r_3 - 4r_1$
$$ \begin{bmatrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{bmatrix} $$
we can get this matrix by doing row interchange (1 and 2) on the identity matrix . This matrix also does the same on other matrix i.e interchanges 1st and 2nd row
$$ \begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 5\end{bmatrix} $$
intuitively this will make $r_3 = 5r_3$
Each elementary matrix $E$ is invertible. The inverse of $E$ is the elementary matrix of the same type that transforms $E$ back into $I$ .