I'm doing practice problems for my exam, but I don't really know how to get this one. I'd like to just be able to understand it before my test if anyone can help explain it!

Prove from the definition of projection (given below) that if projv=u(sub A) then A=A^2 and A=A^T. (Hint: for the latter, show that Ax dot y=x dot Ay for all x,y. It may be helpful to write x and y as the sum of vectors in V and V perp.

Def: Let V in Rm be a subspace, and let b be an element of Rm. We define the projection of b onto V to be the unique vector p that is an element of V with the property that b-p is an element of V-perp. We write p=projv b