sage: A = x.subalgebra_generated_by()
sage: x = A.random_element()
sage: A.one()*x == x and x*A.one() == x
sage: A = x.subalgebra_generated_by()
sage: x = A.random_element()
sage: A.one()*x == x and x*A.one() == x
sage: A = x.subalgebra_generated_by()
sage: actual = A.one().operator().matrix()
sage: expected = matrix.identity(A.base_ring(), A.dimension())
sage: A = x.subalgebra_generated_by()
sage: actual = A.one().operator().matrix()
sage: expected = matrix.identity(A.base_ring(), A.dimension())