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The following code:

documentclass[tikz,border=1mm]{standalone}



usepackage{tikz}

usetikzlibrary{matrix, positioning}



tikzset{

  matrixstyle/.style={

    matrix of nodes,

    nodes={

      draw

    }

}}



begin{document}

    begin{tikzpicture}



        matrix (M) [matrixstyle]{

            .1 & .1 \

            .1 & .1 \

        };



        begin{scope} [local bounding box=MA, shift={(M.west)}, left = 0cm of M.west]

            matrix (M11) [matrixstyle]{

                .1 & .0  \

                .5 & .0 \

            };

            matrix (M12) [matrixstyle, right = 0cm of M11]{

                .2 & .0  \

                .3 & .9 \

            };

            matrix (M21) [matrixstyle, below = 0cm of M11]{

                .0 & .0  \

                .0 & .2 \

            };

            matrix (M22) [matrixstyle, right = 0cm of M21]{

                .3 & .0  \

                .3 & .9 \

            };

        end{scope}



        matrix (N) [matrixstyle, left = 1cm of MA.west]{

            .2 & .2  \

            .2 & .2 \

        };



    end{tikzpicture}

end{document}

produces the following output:

The output should show six matrices. Four in the middle. And one matrix each on the right and left side of the matrix array. However, I did not manage to place the matrix M to the right of the matrix array MA. The error is probably in the following line

begin{scope} [local bounding box=MA, shift={(M.west)}, left = 0cm of M.west]

What is the right way to do it? Why does my approach not work?

Although not exactly the same, something very similar can be done with some tabular and without TiKZ.

documentclass{article}



newcommand{mytab}[4]{%

    begin{tabular}[c]{|c|c|}

        hline

     #1&#2\hline

     #3&#4\hline

    end{tabular}}



begin{document}



mytab{.2}{.2}{.2}{.2}  

begin{tabular}[c]{cccc}

mytab{.1}{.0}{.5}{.2} & mytab{.1}{.1}{.1}{.1}

\[.5cm]

mytab{.0}{.0}{.0}{.2} & mytab{.3}{.0}{.3}{.9} 

end{tabular} 

mytab{.2}{.0}{.3}{.9} 

end{document}

EDIT: or even better with ytableau package

documentclass{article}

usepackage{ytableau}



newcommand{mytab}[4]{%

    begin{ytableau}

     #1&#2\

     #3&#4\

    end{ytableau}}



begin{document}

ytableausetup{centertableaux}



mytab{.2}{.2}{.2}{.2}  

begin{tabular}[c]{cccc}

mytab{.1}{.0}{.5}{.2} & mytab{.1}{.1}{.1}{.1}

\[.5cm]

mytab{.0}{.0}{.0}{.2} & mytab{.3}{.0}{.3}{.9} 

end{tabular} 

mytab{.2}{.0}{.3}{.9} 

end{document}

like this?

matrices you can consider as nodes, so their positioning is with positioning library is straightforward:

documentclass[tikz,border=1mm]{standalone}

usetikzlibrary{matrix, positioning}



begin{document}

    begin{tikzpicture}[

     node distance = 1mm and 2mm,

every matrix/.style = {matrix of nodes,

                      nodes={draw},

                      column sep=-pgflinewidth,

                      row sep=-pgflinewidth}

                        ]

matrix (m1) 

{

.2 & .2  \

.2 & .2 \

};

matrix (m11) [above right=of m1.east]

{

.1 & .0  \

.5 & .0 \

};

matrix (m12) [right=of m11]

{

.1 & .1 \

.1 & .1 \

};

matrix (m21) [below right= of m1.east]

{

.0 & .0  \

.0 & .2 \

};

matrix (m22) [right = of m21]{

.3 & .0  \

.3 & .9 \

};



matrix (m2) [right = of m1 -| m12.east]

{

.2 & .0  \

.3 & .9 \

};

    end{tikzpicture}

end{document}