\begin{graph}
    rankdir=LR
    node [shape=plaintext]
    [[1 0 0 ; 0 1 0 ; 0 0 1]]  
    [[1 0 0 ; 0 1 0 ; 0 0 1]]   -> v_2 [label=  [1 0 ; 0 1]  , color=forestgreen]
    v_2 -> v_3 [label=$S \subseteq \{1,2,3\}^4$(2)]
    v_3 -> [[1 0 0 ; 0 1 0 ; 0 0 1]]  [label=$(f \circ g)^{-1}$(2)]
\end{graph}




\begin{graph}
    rankdir=LR
    node [shape=plaintext]
    $ [[1 0 0 ; 0 1 0 ; 0 0 1]] $(5) 
    $ [[1 0 0 ; 0 1 0 ; 0 0 1]] $(5)   -> v_2 [label=$ [[1 0 ; 0 1]] $(6), color=forestgreen]
    $v_2$(1) -> v_3 [label=$S \subseteq \{1,2,3\}^4$(2)]
    $v_3$(1) -> $ [[1 0 0 ; 0 1 0 ; 0 0 1]] $(5)  [label=$(f \circ g)^{-1}$(2)]
\end{graph}