Notice that f is a linear transformation.
for(1), you need to find the matrix correspondding to f.
for(2), find the four image of the four vertex of each unit square.
let f : be defined by f(x,y) = (x+y, 2x+ay) where a R is a constant.
(a) Show that df(x,y) is invertible if and only if a 2
(b) Examine the image through f of the unit square Q :={(x,y) [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...