[
begin{pmatrix}[ccc|c]
1&2&0&0\
-1&1&2&0\
1&0&1&5\
0&-2&1&4
end{pmatrix}
]
[
begin{pmatrix}[ccc|c]
1&2&0&0\
0&3&2&0\
0&-2&1&5\
0&-2&1&4
end{pmatrix}
]

documentclass{article}
begin{document}
[
left(begin{array}{@{}ccc|c@{}}
     1 &  2 & 0 & 0 \
    -1 &  1 & 2 & 0 \
     1 &  0 & 1 & 5 \
     0 & -2 & 1 & 4
end{array}right)
sim
left(begin{array}{@{}ccc|c@{}}
    1 &  2 & 0 & 0 \
    0 &  3 & 2 & 0 \
    0 & -2 & 1 & 5 \
    0 & -2 & 1 & 4
end{array}right)
]
end{document}

documentclass{article}
newenvironment{rowequmat}[1]{left(array{@{}#1@{}}}{endarrayright)}
begin{document}
[
begin{rowequmat}{ccc|c}
     1 &  2 & 0 & 0 \
    -1 &  1 & 2 & 0 \
     1 &  0 & 1 & 5 \
     0 & -2 & 1 & 4
end{rowequmat}
sim
begin{rowequmat}{ccc|c}
    1 &  2 & 0 & 0 \
    0 &  3 & 2 & 0 \
    0 & -2 & 1 & 5 \
    0 & -2 & 1 & 4
end{rowequmat}
]
end{document}

documentclass{article}
usepackage{amsmath}
usepackage{array}

newenvironment{redmatrix}
  {left(array{@{}rrr|c@{}}}
  {endarrayright)}
newenvironment{ropmatrix}
  {array{@{}c@{}}}
  {endarray}
newcommandopone[2]{xrightarrow{(#1)times r_#2}}
newcommandoptwo[3]{xrightarrow{r_#1{}+{} #2r_#3}}

begin{document}
begin{alignat*}{5}
&
begin{redmatrix}
1&2&0&0\
-1&1&2&0\
1&0&1&5\
0&-2&1&4
end{redmatrix}
&
begin{ropmatrix}
optwo{1}{}{2}
end{ropmatrix}
&
begin{redmatrix}
1&2&0&0\
0&3&2&0\
0&-2&1&5\
0&-2&1&4
end{redmatrix}
&
begin{ropmatrix}
opone{1/3}{2}
end{ropmatrix}
&
begin{redmatrix}
1&2&0&0\
0&1&2/3&0\
0&-2&1&5\
0&-2&1&4
end{redmatrix}\
&&
begin{ropmatrix}
optwo{3}{2}{2}\
optwo{4}{2}{2}\
end{ropmatrix}
&
begin{redmatrix}
1&2&0&0\
0&1&2/3&0\
0&0&7/3&5\
0&0&7/3&4
end{redmatrix}
&
begin{ropmatrix}
opone{3/7}{3}
end{ropmatrix}
&
begin{redmatrix}
1&2&0&0\
0&1&2/3&0\
0&0&1&15/7\
0&0&7/3&4
end{redmatrix}
end{alignat*}

end{document}

documentclass{article}
usepackage{array}
begin{document}
[
left(begin{array}{@{}rrr|c@{}}
1&2&0&0\
-1&1&2&0\
1&0&1&5\
0&-2&1&4
end{array}right)
quad
left(begin{array}{@{}rrr|c@{}}
1&2&0&0\
0&3&2&0\
0&-2&1&5\
0&-2&1&4
end{array}right)
]
end{document}