We show that an often used example of a cohomology algebra with non-vanishing triple Massey product is intrinsically A₃-formal and therefore, in fact, cannot be realized as the cohomology of a differential graded algebra with non-vanishing triple Massey product. We prove this result by computing the graded Hochschild cohomology group which contains the potential obstruction to the vanishing.

We thank Mads Hustad Sandoy for helpful conversations. We are grateful to the anonymous referee for comments and suggestions that helped to improve the manuscript.