Prove that the composition of two linear fractional

Question

Question: 1. Prove that the composition of two linear fractional transformations is a linear fractional transformation.

2. Prove that every linear fractional transformation has an inverse, and that this inverse is also a linear fractional transformation. (T∗ is an inverse of T if T ΟT∗ and T∗ ΟT are both the identity mapping, taking each point to itself.)

3. Show that there is no linear fractional transformation mapping the open disk |z|²/4+v² = 1/16.