1.25:

A homomorphism f : Z₆ ---> Z₆ is uniquely determined by f(1), because, e.g., f(2)=f(1+1)=f(1)+f(1), and, more generally, f(k)=k f(1). If we write f(1) = a, then f(x)=ax for every x. It is easy to show that f is a homomorphism for any choice of a. If a = 0, 2, or 4, then f(3)=0=f(0), so f is not an isomorphism. Similarly, if a=3, f(2)=0=f(0) so f is not an isomorphism. If a = 1 then f is the identity function, an isomorphism. If a = 5, then f o f is equal to the identity (since 5² = 1), so f is an isomorphism.