Chapter 3.3, Problem 16E

Prove that each of the following subsets $H$ of $GL(2,C)$ is subgroup of the group $GL(2,C)$, the general linear group of order $2$

over $C$

a. $H=\left\{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right],\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\right\}$

b. $H=\left\{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cc}i& 0\\ 0& -i\end{array}\right],\left[\begin{array}{cc}-i& 0\\ 0& i\end{array}\right],\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\right\}$