John B

Trying to prove that the proper orthogonal group SO(3) acts transitively on the set of points on the surface of a sphere. Can show that if you assume 2 points on the sphere can be related by x=Ay where A is a 3x3 matrix then A multiplied by its transpose must be I but this only shows A would be in O(3) not SO(3) - i.e. how can you show any 2 points can be linked by A where det(A) = 1? Any help would be much appreciated!