1. The problem statement, all variables and given/known data let [tex]K[/tex] be a field and [tex]K(t)[/tex] the rational functions in [tex]t[/tex]. Show that [tex]\ G=Aut_K K(t)[/tex] [tex]\cong[/tex] [tex]\ GL(2,K)[/tex] 2. Relevant equations I have the fundamental Galois theorem to work with and normal subgroups. but we haven't done splitting fields. 3. The attempt at a solution I am really just unsure of how to proceed here. I am guessing [tex]GL(2,K)[/tex] is just the 2x2 matrices with nonzero determinants and elements in [tex]K[/tex]. and if that's true I don't really know what to do.