A magma is left invertible provided that the rows of its Cayley table are permutations.

The IsLeftInvertible command returns true if the given magma is left invertible, and returns false otherwise.

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

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

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

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

$\mathrm{true}$

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

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

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

$\mathrm{false}$

The Magma[IsLeftInvertible] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.