Discussion
How many fixed points does a bilinear transformation have, other than the identity?
Answer: A
Setting \( w = z \) gives
\[ cz^{2} + (d - a)z - b \;=\; 0, \]
a quadratic, so there are at most two roots. A repeated root gives one fixed point, and the identity is the degenerate case fixing everything. Being determined by three point-images is a separate property, and is where the count of three belongs
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