Solution
= Solution
The <transpose> reverses product order, so $(CB)^{\mathsf T}=B^{\mathsf T}C^{\mathsf T}$. If $B$ is an <orthogonal matrix>, then $B^{-1}=B^{\mathsf T}$ and the given identity becomes
$$
B^{\mathsf T}(C^{\mathsf T}+C)=0.
$$
Multiply on the left by $B$ to obtain $C^{\mathsf T}+C=0$. Therefore \b[$C$ is antisymmetric], so it is an <antisymmetric matrix>, namely $\boxed{C^{\mathsf T}=-C}$.