I want to prove that every orientation reversing motion of $\mathbb{E}^2$ is a composite of a half-turn and a reflection. The orientation reversing motions in $\mathbb{E}^2$ are glides and reflections, where a reflection is a special case of a glide. I have proved that every glide is a composite of half-turn and a reflection. Now i am doubtfull that i proved that every orientation reversing motion of $\mathbb{E}^2$ is a composite of a half-turn and a reflection. Do i also have to look at rotations with $det(A)=-1$?
Thank you!