\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}

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