Show that (3,1), (-2,-1), and (4,3) generate the additive group Z x Z.
note that (3,1) + (-2,-1) (1,0) note that -2*(-2,-1) + -(4,3) (0,1) Since (1,0) and (0,1) form a basis for Z^2 and are generated by the additive group, it follows that the group generates all of Z^2. QED.
