Inverse of Möbius transform - w(z)?

[Jaynte]

Homework Statement

I want to know how I could extract T from Tz in matrix form so I can
get $$T^{-1}$$ to get the inverse of w(z).

w(z)=Tz=$$\frac{az+b}{cz+d}$$

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

You can't. The moebius transform is not linear and only linear transforms can be written as matrices.

 

[Jaynte]

Thanks.

So how how do I solve it if I don't want to remember the answer $$z(w)=\frac{-dw+b}{cw-a}?$$

 

[Dick]

You invert it like you invert any other function. If w=(az+b)/(cz+d), solve that equation for z using algebra.

 

[Jaynte]

Of course, I am to tired now I should go to sleep :) Thank you.