Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 302 / 1 / a / Solution

The matrices are rotations about the third coordinate axis. Direct multiplication givesand $g(\theta {)}^{\mathsf{T}}g(\theta )=I$. Thus they form a one-parameter subgroup of the orthogonal group $O(3)$, isomorphic to the circle group.