let f : $\displaystyle R^2 \rightarrow R^2$ be defined by f(x,y) = (x+y, 2x+ay) where a $\displaystyle \in$ R is a constant.

(a) Show that df(x,y) is invertible if and only if a $\displaystyle \neq$ 2

(b) Examine the image through f of the unit square Q :={(x,y) $\displaystyle \in$ [0,1] x [0,1]} when a=1, a=2, and a=3

So.. I don't understand how to show it's invertible or what (b) even means...