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Prove: The cross ratio of four points z1, z2, z3, z4 is invariant under a bilinear transformation i.e. if w1, w2, w3, w4 are, respectively, the images of z1, z2, z3, z4 under a bilinear transformation, then the cross ratio of w1, w2, w3, w4 must equal the cross ratio of z1, z2, z3, z4. In other words, prove


             ole.gif


Proof. Starting with


             ole1.gif


we first observe that


             ole2.gif


Consequently,



ole3.gif  



                                     ole4.gif


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