Classification of constant solutions of the associative Yang–Baxter equation on $\operatorname{Mat}_3$

We find all nonequivalent constant solutions of the classical associative Yang–Baxter equation for $\operatorname{Mat}_3$. New examples found in the classification yield the corresponding Poisson brackets on traces, double Poisson brackets on a free associative algebra with three generators, and anti-Frobenius associative algebras.