Problem 1766 (difficulty: 5/10)

Let \(\displaystyle H\) be the upper half-plane. Prove that

\(\displaystyle \Aut(H)= \left\{ T(z)=\frac{az+b}{cz+d}, \ a, \ b,\ c,\ d\in \RR , \,\, \det\begin{pmatrix}a&b\\ c&d\end{pmatrix}>0 \right\} = PSL(2,\RR). \)

If an element of \(\displaystyle \Aut(H)\) is represented by a matrix \(\displaystyle \begin{pmatrix} a & b\\ c & d \end{pmatrix}\) what matrices correspond to the same map?

Give me another random problem!