The HasIdentity command returns true if the given magma has a two-sided identity element. That is, an element i such that i*x = x*i = x, for all x in m.  Otherwise, it returns the value false.

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

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

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

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

$\mathrm{true}$

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

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

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

$\mathrm{false}$

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

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