$$ begin{tikzcd} koplus k^2 arrow[r] & koplus k^2 & 0oplus k arrow[l] end{tikzcd} $$

documentclass{article}
usepackage{mathtools}
usepackage{tikz-cd}
usepackage{etoolbox}

makeatletter
letxsmallmatrixsmallmatrix
letendxsmallmatrixendsmallmatrix
patchcmd{xsmallmatrix}{6ex@}{12ex@}{}{}
newenvironment{bxsmallmatrix}
 {left[xsmallmatrix}
 {endxsmallmatrixright]}
makeatother

begin{document}

[
begin{tikzcd}[ampersand replacement=&,column sep=huge]
koplus k^2
arrow[r,"{begin{bxsmallmatrix}1&0&0\0&1&1\0&0&1end{bxsmallmatrix}}"]
&
koplus k^2
&
0oplus k arrow[l,"{begin{bxsmallmatrix}0&0\0&1\0&1end{bxsmallmatrix}}"']
end{tikzcd}
]

[
begin{tikzcd}[ampersand replacement=&,column sep=huge]
koplus k^2
arrow[r,"{begin{bsmallmatrix}1&0&0\0&1&1\0&0&1end{bsmallmatrix}}"]
&
koplus k^2
&
0oplus k arrow[l,"{begin{bsmallmatrix}0&0\0&1\0&1end{bsmallmatrix}}"']
end{tikzcd}
]

end{document}

documentclass[11pt]{article}
usepackage{mathtools}
usepackage{tikz-cd}

begin{document}

[
 begin{tikzcd}[row sep=1.2cm, column sep=2cm, arrows=-stealth, ampersand replacement=&]
  koplus k^2rar{begin{bsmallmatrix}1 & 0 & 0\0 & 1 & 1\0 & 0 & 1end{bsmallmatrix}} & koplus k^2& lar[swap]{begin{bsmallmatrix}0 & 0\0 & 1\ 0 & 1end{bsmallmatrix}} 0oplus k
   end{tikzcd}
]

end{document}

[ renewcommand{arraystretch}{0.7}setlength{arraycolsep}{3pt}
     begin{tikzcd}[row sep=1.2cm, column sep=2cm, arrows=-stealth, ampersand replacement=&]
      koplus k^2rar{begin{bmatrix}1 & 0 & 0\0 & 1 & 1\0 & 0 & 1end{bmatrix}} & koplus k^2& lar[swap]{begin{bmatrix}0 & 0\0 & 1\ 0 & 1end{bmatrix}} 0oplus k
       end{tikzcd}
    ]

documentclass{standalone}

usepackage{amsmath}

usepackage{tikz}
    usetikzlibrary{calc}

begin{document}
begin{tikzpicture}
node (A) {$koplus k^2$};
node (B) at ($(A)+(3,0)$) {$koplus k^2$};
node (C) at ($(B)+(3,0)$) {$0oplus k$};
%
draw[-stealth]
    (A) -- (B)
    node[midway,above,scale=.5]
        {$begin{bmatrix}
            1& 0& 0\
            0& 1& 0\
            0& 0& 1
          end{bmatrix}$};
draw[-stealth]
    (C) -- (B)
    node[midway,above,scale=.5]
        {$begin{bmatrix}
            0& 0\
            0& 1\
            0& 1
          end{bmatrix}$};
end{tikzpicture}
end{document}