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\begin{document}

\begin{center} \textbf{Square Symmetries Multiplication Table.} \end{center}


\begin{eqnarray*}
I:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] &  & R:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
4 & 1  \\ 3 & 2
\end{array} \right ] \\ \\
R^2:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
3 & 4  \\ 2 & 1
\end{array} \right ] &  & R^3:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
2 & 3  \\ 1 & 4
\end{array} \right ] \\
\\
V:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
2 & 1  \\ 3 & 4
\end{array} \right ] &  & H:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
4 & 3  \\ 1 & 2
\end{array} \right ] \\ \\
U:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
3 & 2 \\ 4 & 1
\end{array} \right ] &  & L:  \left [ \begin{array}{cc}
1 & 2  \\ 4 & 3
\end{array} \right ] \rightarrow  \left [ \begin{array}{cc}
1 & 4  \\ 2 & 3
\end{array} \right ] \\
\end{eqnarray*}

\

\begin{center}
\begin{tabular}{|c||c|c|c|c|c|c|c|c|}
\hline
 & $I$ & $R$  &  $R^2$ & $R^3$ & $V$  & $H$  & $U$  & $L$  \\
\hline
\hline
$I$ & $I$ & $R$  &  $R^2$ & $R^3$ & $V$  & $H$  & $U$  & $L$   \\
\hline
$R$ & $R$ & $R^2$  &  $R^3$ & $I$ & $U$  & $L$  & $H$  & $V$  \\
\hline
$R^2$ & $R^2$ & $R^3$  &  $I$ & $R$ & $H$  & $V$  & $L$  & $U$  \\
\hline
$R^3$ & $R^3$ & $I$  &  $R$ & $R^2$ & $L$  & $U$  & $V$  & $H$  \\
\hline
$V$ & $V$ & $L$  &  $H$ & $U$ & $I$  & $R^2$  & $R$  & $R^3$  \\
\hline
$H$ & $H$ & $U$  &  $V$ & $L$ & $R^2$  & $I$  & $R^3$  & $R$  \\
\hline
$U$ & $U$ & $V$  &  $L$ & $H$ & $R^3$  & $R$  & $I$  & $R^2$  \\
\hline
$L$ & $L$ & $H$  &  $U$ & $V$ & $R$  & $R^3$  & $R^2$  & $I$  \\
\hline
\end{tabular}
\end{center}




\end{document}