Show all algebraic group homomorphisms between $GL_1\to GL_1$ are given by $z\mapsto z^n$ for $n\in \Bbb{Z}$
Here $GL_1$ denotes the group scheme which is represented by the functor $CAlg_k^{op}\to Grp$ given by $GL_1(R)=R^\times$ for a commutative $k$-algebra $R$. I am not sure how to even start with a problem like this, clearly $R^\times\to R^\times$ the map $r\to r^n$ is indeed a group homomorphism but how do I show that these are the only ones? Thanks for any help.