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
Proof. Starting with
we first observe that
Consequently,
