Chapter 3.13, Problem 4P

Show that the matrices

$\text{I}=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right),A=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right),\text{B}=\left(\begin{array}{cc}0& -1\\ -1& 0\end{array}\right),\text{C}=\left(\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right),$ under matrix multiplication, form a group. Write the group multiplication table to see that this group (called the 4’s group) is not isomorphic to the cyclic group of order 4 in Problem 1. Show that the 4’s group is Abelian but not cyclic.