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\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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