Question

Suppose that V is a vector space over R (not necessarily finite dimensional), and that T1 : V −→ V and T2 : V −→ V are linear transformations from V to V with the property that T3 = T2 ◦ T1 is the identity transformation, i.e. that T3(v) = v for all vectors v in V .
(a) Prove that T1 is injective.
(b) Prove that T2 is surjective.