I am studying this answer by user "Etienne dM". They claim that, because $(AA^+)^T = AA^+$, we have that $A^T(Ax-b) = ((AA^+)A)^Tb - A^Tb = 0$. However, I do not understand how $A^T(Ax-b) = ((AA^+)A)^Tb - A^Tb = 0$ is possible. In particular, it seems like an extra $AA^+$ term comes out of nowhere. I would greatly appreciate it if people would please take the time to explain what's going on here.