Let $\sigma :L\rightarrow L$, s.t $\sigma (\alpha)=\bar{\alpha}$.
I've been asked to show that $\sigma\in Aut(L/K)$(the set of all automorphisms for the field extension) has order 1 or 2.
I'm assuming that the operator on this group is $\circ$, the composition of functions. By order does it just mean the minimum number of times to repeatedly use the function on an $\alpha\in L$ in order to map $\alpha$ to itself. So here either $\sigma(\alpha)=\alpha$ or $\sigma(\sigma(\alpha))=\alpha$. If this is what the question is asking to show, then how would I prove this.