Definition:Möbius Transformation/Also defined as

Möbius Transformation: Also defined as
Some sources, when defining a Möbius transformation, do not insist that $a d - b c \ne 0$.

However, it needs to be pointed out that when $a d - b c = 0$, the resulting mapping is not a bijection.

Also see

 * Möbius Transformation is Bijection