I have a problem in progressing in SNF
We have matrix $A$:
$$A= \begin{bmatrix} 14&3&11\\8&-3&11\\3&3&0 \end{bmatrix} $$
I tried to make the first row zeros except the first one and the same for the first column
I got the following matrix $$ A= \begin{bmatrix} 3&14&11\\0&22&22\\0&-11&-11 \end{bmatrix} $$ Then I stuck here
$$ A= \begin{bmatrix} 3&0&0\\0&0&33\\0&0&-11 \end{bmatrix} $$ The problem is that 3 don't divide all the entries so from here what shall I do . This happens alot to me so I would like to know what shal I do in such situation I don't want an alternative solution .
From the last matrix $A$ (why are they all called $A\ \ddot\frown$?) add row $3$ to row $1$: $$\begin{bmatrix} 3&0&-11\\0&0&33\\0&0&-11 \end{bmatrix},$$ then add four times column $1$ to column $4$: $$\begin{bmatrix} 3&0&1\\0&0&33\\0&0&-11 \end{bmatrix},$$ then swap columns $1$ and $3$: $$\begin{bmatrix} 1&0&3\\33&0&0\\-11&0&0 \end{bmatrix},$$ etc.