The IsIdentity command determines whether an element id of a magma m is an identity for m.  It returns true if id is an identity of m, and returns false otherwise.  The element id is an identity of m if id * x = x = x * id, for all x in m.

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

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

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

$\mathrm{IsIdentity}\left(m\,1\right)$

$\mathrm{true}$

$\mathrm{IsIdentity}\left(m\,2\right)$

$\mathrm{false}$

$\mathrm{IsIdentity}\left(m\,3\right)$

$\mathrm{false}$

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

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