Past exam of the mathematics course of the University of Cambridge / 2008 / ia / Paper 3 / 7E / i / Solution

The assertion is true. A Möbius map fixes infinity if and only if $c=0$: if $c\ne 0$, its value there is the finite number $a/c$. For $c=0$, the decomposition above uses only a nonzero complex scaling and a translation. These maps form the Affine subgroup of the Möbius group.