The IsIdempotent command returns true if the given magma is idempotent, that is, if it satisfies the law X*X = X.  It returns false otherwise.

$\mathrm{with}\left(\mathrm{Magma}\right)\:$

$m≔⟨⟨⟨1\left|1\right|2⟩\,⟨2\left|2\right|3⟩\,⟨1\left|2\right|3⟩⟩⟩$

$m≔\left[\begin{array}{ccc}1& 1& 2\\ 2& 2& 3\\ 1& 2& 3\end{array}\right]$

$\mathrm{IsIdempotent}\left(m\right)$

$\mathrm{true}$

$m≔⟨⟨⟨1\left|2\right|3⟩\,⟨2\left|3\right|3⟩\,⟨3\left|1\right|2⟩⟩⟩$

$m≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 3\\ 3& 1& 2\end{array}\right]$

$\mathrm{IsIdempotent}\left(m\right)$

$\mathrm{false}$

The Magma[IsIdempotent] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.