These prove that isomorphism is an equivalence relation.
(a) Show that the identity map id: V → V is an isomorphism. Thus, any vector space is isomorphic to itself.
(b) Show that if f: V → W is an isomorphism then so is its inverse f-1: W → V. Thus, if V is isomorphic to W then also W is isomorphic to V.
(c) Show that a composition of isomorphism's is an isomorphism: if f: V → W is an isomorphism and g: W → U is an isomorphism then so also is g ◦ f: V → U. Thus, if V is isomorphic to W and W is isomorphic to U, and then also V is isomorphic to U.