4. Proposition 2.6.1 - An operation on Möbius Transformations

Let $f_{1}, f_{2} \in M ö b (C)$ , and we identify them with the matrices:

f_{1} \sim [\begin{matrix} a_{1} & b_{1} \\ c_{1} & d_{1} \end{matrix}] f_{2} \sim [\begin{matrix} a_{2} & b_{2} \\ c_{2} & d_{2} \end{matrix}]

Then by the remark we have that $f_{2} \circ f_{1} \sim$ 1;; $[\begin{matrix} a_{2} & b_{2} \\ c_{2} & d_{2} \end{matrix}] [\begin{matrix} a_{1} & b_{1} \\ c_{1} & d_{1} \end{matrix}]$