Practice problem
Which Möbius transformation sends distinct points a,b,ca,b,ca,b,c in P1\mathbb{P}^1P1 to 0,1,∞0,1,\infty0,1,∞?
z↦a−bc−z/a−zc−bz \mapsto \frac{a-b}{c-z}\bigg/\frac{a-z}{c-b}z↦c−za−b/c−ba−z
z↦a−za−b/c−zc−bz \mapsto \frac{a-z}{a-b}\bigg/\frac{c-z}{c-b}z↦a−ba−z/c−bc−z
z↦a−ba−z/c−bc−zz \mapsto \frac{a-b}{a-z}\bigg/\frac{c-b}{c-z}z↦a−za−b/c−zc−b
Type a concept, like “slope” or “photosynthesis”.