Homotopes of $(-1,1)$-algebras with two generators

We present an example of a $(-1,1)$-algebra that has an isotope which is not an $(-1,1)$-algebra. We prove that the defining relation is preserved by the homotopes of 2-generated $(-1,1)$-algebras and, moreover, that the variety generated by a free $(-1,1)$-algebra of rank 2 is stable under the operation of taking a homotope.