Suppose 3x3 A represents the transformation which projects vectors onto the xz plane.
(So A $[ ]^T$ = $[ 0 y ]^T$.) Explicitly state what A is, giving its entries. Without doing any calculations, what must A2 be? Why?
I'm not sure how to approach this problem, can someone point me in the right direction?
All you have to do is to map $e_1$ to $e_1$,$e_2$ to $0$ and $e_3$ to $e_3$ where $e_1=(1,0,0),e_2=(0,1,0)$ and $e_3=(0,0,1)$. The rows are $(1,0,0),(0,0,0),(0,0,1)$. The square of this matrix is itself. No need to calculate the square: if you project a point to the x-z plane and project it again you get back the same point you got after the first projection.