# Double dot product of two second order tensors using index notation

I am given $$\vec r=x_i\hat e_i$$ where $$r=|\vec r|$$ and the tensors are introduced as: $$\overline{\overline{T}}=\frac{\delta_{ij}\hat e_i\hat e_j}{r}+\frac{x_ix_j \hat e_i\hat e_j}{r^3}$$ and $$\overline{\overline{A}}=\epsilon_{ijk}\frac{\delta}{\delta x_k}(\frac{1}{r})\hat e_i\hat e_j$$. I am asked to calculate the $$\overline{\overline{A}}$$.$$\overline{\overline{T}}$$ and $$\overline{\overline{A}}$$..$$\overline{\overline{T}}$$ which means dot and double dot of these two tensors. I know how to get the expressions, but I am not sure how much I can simplify them. I would appreciate any suggestions regarding that.