Thread: Proving Rotational Matrix Preserves Orientation

Hello,

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?

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)