Game Theory - Mixed strategy ESS

Question

I have a payoff matrix of a symmetric game like this:

$ \begin{matrix} & A & B \\ A & (3, 3) & (1, 2) \\ B & (2, 1) & (5, 5) \end{matrix} $

I found that $(A, A)$ and $(B, B)$ are pure strict NE and also $(\frac{2}{3}, \frac{1}{3})$ is a mixed NE for both players.

Now how can I check if the mixed NE is also an ESS?