Hi I need help with this question, thanks!

3. For the following maps determine whether it is a ring homomorphism, whether it is injective and whether it is surjective. If $ is a homomorphism, determine ker(d). (a) d: Z -+ mZ given by o(n) = mn. You may have to consider different cases depending on the value of me Z. (b) Let R, S be rings and consider the projection m1 : R x S - R given by mi(r, s) = r. (c) $ : Q[x] - M2(Q) defined by $ (f ) = f(0) f'(0) 0 f(0)