Is the subgroup of $GL_3(\mathbb R)$ denoted by $Q=\{A \in GL_3(\mathbb R)\mid AA^t=I_3\}$ cyclic? What's generating it?
I showed $Q$ is a group, and realized it's the group of all orthogonal matrices. My conjecture is that the generating element is some sort of rotation matrix, however it seems that rotation around the x-axis, for instance: \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} Seems to be like it doesn't generate some orthogonal matrices, actually all those that don't have the element 1 in the (3,3) entry...
Thanks in advance for any assistance!