(i) Prove that the cross-ratio [a,b,c,d] is invariant if any two elements and the complementary two elements are trans posed. Prove that
And that
(ii) Letting λ = [a,b,c,d], prove that if λ∈ {∞,0,1}, then any permutation off {a,b,c,d} yields across-ratio in{∞,0,1}, and if λ/∈ {∞,0,1},then the rear eat most the six values
(iii) Prove that the function
Takes a constant value on the six values listed in part(ii).