Question

Show that any automorphism of a field k fixes it’s prime subfield.

Answer 1

Suppose K is a prime subfield of E, then if ϕϕ is an automorphism from E to E, we have for all x ∈∈ K, phi(x)=xphi(x)=x.

I feel like this is just the definition of a field automorphism, but my book says this should be proven as an exercise.