It would also suffice to prove
R(u X v) = det(R)(Ru X Rv)
Since the det(R) = 1 for all R SO(3)
I'm trying to prove a specific lemma, one that shows that
R(u X v) = Ru X Rv
R SO(3) is a special orthogonal rotation matrix;
u,v are vectors;
and X is the cross product.
Do I need to prove this using direct calculation, expanding and expanding.. I've tried and it gets quite large and unmanageable for me. Are there any other tricks I could try?