(a) prove the identity map is an isomorphism (i.e., that it's linear and bijective).
(b) isomorphisms are bijective. bijective maps have inverses. prove if a linear map T has an inverse T^{-1}, that T^{-1} is linear.
(c) prove that the composition of two linear isomorphisms is again a linear isomorphism.
let me know if you have trouble with these.