For the Identity matrix $(\mathbf{I_4})$,
Applying the row operation(s):
$2\cdot R_1 - R_3 \rightarrow R_3 $,
Would give the following matrix:
$$\begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 2&0&-1&0 \\ 0&0&0&1 \\ \end{pmatrix} $$.
But this matrix isn't an elementary matrix, as there are essentially 2 row operations being performed right?
If not, what would the row operation be, to find the inverse of the elementary matrix?