Is it right to switch rows after adding one row to another in row transformation ?

Question

I wanted to find the rank of the matrix, I ended up in this matrix after doing some row transformations :

$\begin{pmatrix} 1 & 4 & 1 & 4 \\ 0 & 0 & 3 & 2 \\ 0 & 3 & 5 & 6 \\ 0 & 0 & 0 & 0 \\ \end{pmatrix}$

Is it right to switch any two rows now, i.e R2 <-> R3 so they become upper triangular and I get rank 3 ? Or should the switching of rows be done before doing addition of rows?