Solution
= Solution
The other element is $\boxed{-M}$. Conjugation by $M$ and $-M$ is identical, so the homomorphism $SU(2)\to SO(3)$ has kernel $\{\pm I\}$ and is the <Spin group> double cover.
= Solution
The other element is $\boxed{-M}$. Conjugation by $M$ and $-M$ is identical, so the homomorphism $SU(2)\to SO(3)$ has kernel $\{\pm I\}$ and is the <Spin group> double cover.