\documentstyle{jarticle}
\begin{document}

\begin{eqnarray*}
\left(\begin{array}{rrr}5&3&8\\8&5&8\\3&4&5\end{array}\right.\left|\begin{array}{rrr}1&0&0\\0&1&0\\0&0&1\end{array}\right)
% (0) = 1/5*(0)
&\overrightarrow{(0) = \frac{1}{5}\times(0)}&
\left(\begin{array}{rrr}1&\frac{3}{5}&\frac{8}{5}\\8&5&8\\3&4&5\end{array}\right.\left|\begin{array}{rrr}\frac{1}{5}&0&0\\0&1&0\\0&0&1\end{array}\right)\\
% (1) = (1) -8*(0)
&\overrightarrow{(1) = (1) -8\times(0)}&
\left(\begin{array}{rrr}1&\frac{3}{5}&\frac{8}{5}\\0&\frac{1}{5}&-\frac{24}{5}\\3&4&5\end{array}\right.\left|\begin{array}{rrr}\frac{1}{5}&0&0\\-\frac{8}{5}&1&0\\0&0&1\end{array}\right)\\
% (2) = (2) -3*(0)
&\overrightarrow{(2) = (2) -3\times(0)}&
\left(\begin{array}{rrr}1&\frac{3}{5}&\frac{8}{5}\\0&\frac{1}{5}&-\frac{24}{5}\\0&\frac{11}{5}&\frac{1}{5}\end{array}\right.\left|\begin{array}{rrr}\frac{1}{5}&0&0\\-\frac{8}{5}&1&0\\-\frac{3}{5}&0&1\end{array}\right)\\
% (1) = 5*(1)
&\overrightarrow{(1) = 5\times(1)}&
\left(\begin{array}{rrr}1&\frac{3}{5}&\frac{8}{5}\\0&1&-24\\0&\frac{11}{5}&\frac{1}{5}\end{array}\right.\left|\begin{array}{rrr}\frac{1}{5}&0&0\\-8&5&0\\-\frac{3}{5}&0&1\end{array}\right)\\
% (2) = (2) -11/5*(1)
&\overrightarrow{(2) = (2) -\frac{11}{5}\times(1)}&
\left(\begin{array}{rrr}1&\frac{3}{5}&\frac{8}{5}\\0&1&-24\\0&0&53\end{array}\right.\left|\begin{array}{rrr}\frac{1}{5}&0&0\\-8&5&0\\17&-11&1\end{array}\right)\\
% (2) = 1/53*(2)
&\overrightarrow{(2) = \frac{1}{53}\times(2)}&
\left(\begin{array}{rrr}1&\frac{3}{5}&\frac{8}{5}\\0&1&-24\\0&0&1\end{array}\right.\left|\begin{array}{rrr}\frac{1}{5}&0&0\\-8&5&0\\\frac{17}{53}&-\frac{11}{53}&\frac{1}{53}\end{array}\right)\\
% (0) = (0) -3/5*(1)
&\overrightarrow{(0) = (0) -\frac{3}{5}\times(1)}&
\left(\begin{array}{rrr}1&0&16\\0&1&-24\\0&0&1\end{array}\right.\left|\begin{array}{rrr}5&-3&0\\-8&5&0\\\frac{17}{53}&-\frac{11}{53}&\frac{1}{53}\end{array}\right)\\
% (0) = (0) -16*(2)
&\overrightarrow{(0) = (0) -16\times(2)}&
\left(\begin{array}{rrr}1&0&0\\0&1&-24\\0&0&1\end{array}\right.\left|\begin{array}{rrr}-\frac{7}{53}&\frac{17}{53}&-\frac{16}{53}\\-8&5&0\\\frac{17}{53}&-\frac{11}{53}&\frac{1}{53}\end{array}\right)\\
% (1) = (1) +24*(2)
&\overrightarrow{(1) = (1) +24\times(2)}&
\left(\begin{array}{rrr}1&0&0\\0&1&0\\0&0&1\end{array}\right.\left|\begin{array}{rrr}-\frac{7}{53}&\frac{17}{53}&-\frac{16}{53}\\-\frac{16}{53}&\frac{1}{53}&\frac{24}{53}\\\frac{17}{53}&-\frac{11}{53}&\frac{1}{53}\end{array}\right)\\
\left(\begin{array}{rrr}-\frac{7}{53}&\frac{17}{53}&-\frac{16}{53}\\-\frac{16}{53}&\frac{1}{53}&\frac{24}{53}\\\frac{17}{53}&-\frac{11}{53}&\frac{1}{53}\end{array}\right)\left(\begin{array}{rrr}5&3&8\\8&5&8\\3&4&5\end{array}\right)&=&\left(\begin{array}{rrr}1&0&0\\0&1&0\\0&0&1\end{array}\right)
\end{eqnarray*}
\end{document}

