# Question about finding pivot columns in a matrix

I for the most part understand the idea of the pivot column, but I'm slightly confused. I know a pivot is the leading coefficient in a column with all the rows below containing 0's. However do the pivots have to be along the diagonal? For example here the only pivot column would be the one containing the two, correct?

\begin{matrix} 2 & 3 & \\ 0 & 0 & \\ 0 & 0 & \\ \end{matrix}

Also for here only the column with the two would be a pivot column? \begin{matrix} 2 & 3 & 6 \\ 0 & 0 & 0 \\ \end{matrix}