Find the projection matrix for the projection onto the null space of $$A = \begin{pmatrix}1&2&3\\ 2&4&6\\ -1&-2&-3\end{pmatrix}$$
I know the formula to find the projection is $$A\,(A^T\, A)^{-1}\, A^T$$
I'm having trouble getting started. There is a hint in the homework that there will be $2$ columns instead of $3$. How is that?
Any help would be appreciated.