What is meant by an inversion in a circle in $\mathbb{C} \cup\{\infty\}$ ? Show that a composition of two inversions is a Möbius transformation.

Hence, or otherwise, show that if $C^{+}$and $C^{-}$are two disjoint circles in $\mathbb{C}$, then the composition of the inversions in $C^{+}$and $C^{-}$has two fixed points.