Mobius transformations — $L^{-1} \times M\lbrace0,1,\infty\rbrace\times L$

Question

$$L^{-1} \times M\lbrace0,1,\infty\rbrace\times L$$

I cannot seem to get the right answer when I multiple them out.

$$(1-i)z \cdot (1-z) \cdot \frac{z}{1-i}$$

What do you get when you multiple these out?