In this talk, we consider the multiplication operator $M_{z_{1}^{n}z_{2}^{n}}$ on a certain closed subspace $L_{a,\alpha}^{2++}(A_{r}^{2})$ of weighted Bergman spaces $L_{a,\alpha}^{2}(A_{r}^{2})$ over the biannulus $A^{2}_{r}$. We prove that the operator $M_{z_{1}^{n}z_{2}^{n}}$ is similar to $\bigoplus\limits_{1}^{n^2}M_{z_{1}z_{2}}$ on $L_{a,\alpha}^{2++}(A_{r}^{2})$. Moreover, the reducing subspaces of $M_{z_{1}^{n}z_{2}^{n}}$ are investigated.

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