Is it possible to arrange $p^2$ points on $p^2$ lines so that there are $p$ points on each line?

Question

There are $p^2$ points and $p^2$ lines. Two lines have no more than one intersection point. Is it possible (for any $p$) to arrange the points so that there are $p$ points on each line?

For example, for $p=2$ it is possible.