I am giving $$A=\{1,i,-1,-i\}$$ and $$B=\{\begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix}, \begin{pmatrix} 0 & -1 \\ 1 & \phantom{-}0\end{pmatrix}, \begin{pmatrix} -1 & \phantom{-}0 \\ \phantom{-}0 & -1\end{pmatrix}, \begin{pmatrix} \phantom{-}0 & 1 \\ -1 & 0\end{pmatrix}\}$$
- Show that $A$ is a group.
- Make a Cayley table.
- Show that it is cyclic.
- Find all subgroups.
- Find generators for the group and the subgroups.
I have done this for $A$ but how should I do $B$ with matrices?