  We study matrices of morphisms preserving the family of words coding
3-interval exchange transformations. It is well known that matrices of
morphisms preserving sturmian words (i.e. words coding 2-interval exchange
transformations with the maximal possible factor complexity) form the monoid
$\{\boldsymbol{M}\in\mathbb{N}^{2\times 2} | \det\boldsymbol{M}=\pm1\} =
\{\boldsymbol{M}\in\mathbb{N}^{2\times 2} |
\boldsymbol{M}\boldsymbol{E}\boldsymbol{M}^T = \pm\boldsymbol{E}\}$, where
$\boldsymbol{E} = (\begin{smallmatrix}0&1 -1&0\end{smallmatrix})$.
  We prove that in case of exchange of three intervals, the matrices preserving
words coding these transformations and having the maximal possible subword
complexity belong to the monoid $\{\boldsymbol{M}\in\mathbb{N}^{3\times 3} |
\boldsymbol{M}\boldsymbol{E}\boldsymbol{M}^T = \pm\boldsymbol{E},\
  \det\boldsymbol{M}=\pm 1\}$, where $\boldsymbol{E} =
\Big(\begin{smallmatrix}0&1&1 -1&0&1 -1&-1&0\end{smallmatrix}\Big)$.
