The IsAntiCommutative command returns true if the given magma is anti-commutative, that is, if X*Y = Y*X only if X = Y. It returns false otherwise.

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

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

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

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

$\mathrm{true}$

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

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

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

$\mathrm{false}$

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

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