# a group

SL_2(Z_3)

Group $SL_2(\Bbb Z_3)$:

$a=\left(\begin{array}{cc}0&1\\2&0\end{array}\right)$, $b=\left(\begin{array}{cc}0&1\\2&1\end{array}\right)$, $ba^3b=\left(\begin{array}{cc}0&1\\2&2\end{array}\right)$

$a^3=\left(\begin{array}{cc}0&2\\1&0\end{array}\right)$, $bab=\left(\begin{array}{cc}0&2\\ 1&1\end{array}\right)$, $a^2b=\left(\begin{array}{cc}0&2\\1&2\end{array}\right)$

$e=\left(\begin{array}{cc}1&0\\ 0&1\end{array}\right)$, $a^2ba=\left(\begin{array}{cc}1&0\\ 1&1\end{array}\right)$, $(ba)^2=\left(\begin{array}{cc}1&0\\2&1\end{array}\right)$

$(ab)^2=\left(\begin{array}{cc}1&1\\0&1\end{array}\right)$, $b^2ab=\left(\begin{array}{cc}1&1\\ 1&2\end{array}\right)$, $a^3ba=\left(\begin{array}{cc}1&1\\2&0\end{array}\right)$

$a^3b=\left(\begin{array}{cc}1&2\\0&1\end{array}\right)$, $a^2b^2=\left(\begin{array}{cc}1&2 \\1&0\end{array}\right)$, $bab^2=\left(\begin{array}{cc}1&2\\2&2\end{array}\right)$

$a^2=\left(\begin{array}{cc}2&0\\ 0&2\end{array}\right)$, $ab^2=\left(\begin{array}{cc}2&0\\ 1&2\end{array}\right)$, $ba=\left(\begin{array}{cc}2&0\\ 2&2\end{array}\right)$

$ab=\left(\begin{array}{cc}2&1\\ 0&2\end{array}\right)$, $b^2aba=\left(\begin{array}{cc}2&1\\ 1&1\end{array}\right)$, $b^2=\left(\begin{array}{cc}2&1\\2&0\end{array}\right)$

$b^2a=\left(\begin{array}{cc}2&2\\0&2\end{array}\right)$, $aba=\left(\begin{array}{cc}2&2\\1&0\end{array}\right)$, $abab^2=\left(\begin{array}{cc}2&2\\2&1\end{array}\right)$