Non-realizability of a triple Massey product for the algebra ${\mathbb{F}}_2[a,b,c]\mathrm{/}(ab,bc)$

We show that an often used example of a cohomology algebra with non-vanishing triple Massey product is intrinsically A_3-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.