1. The problem statement, all variables and given/known data Given a transformation of the plane F(x,y) = (2x+y,x-2y), find F-1. 2. Relevant equations Actually this exercise had an item (a) which I had to prove this is a transformation. So I proved this function is injective and surjective. I know F(x,y) = (u,v) IFF F-1(u,v) = (x,y). 3. The attempt at a solution I did it, but I don't know if this is the real solution... F(x,y) = (u,v) IFF F-1(u,v) = (x,y). u = 2x + y v = x - 2y Solving this, I concluded that: x = (v+2u)/5 and y = (u-2v)/5 Is this the solution? F-1 = ((v+2u)/5, (u-2v)/5) or do I have to do anything else?