Suppose U -> V -> W, with transformations T (U to V) and S (V to W).

1) Suppose ST is one-to-one and T is onto, show that S is one-to-one.

My answer 1)

Suppose (ST)(u) is one-to-one, and suppose T is onto:

(ST)(u) = S(T(0)) = 0 = S(T(u)) = S(v)

Therefore v = 0.

2) Suppose ST is onto and S is one-to-one, show that T is onto.

This one has me beat and I'm not sure how to approach it at all.

Can someone please (hopefully) verify that I did 1) correctly, and help with 2)?

Thank you!