I'm not sure that I have the grasp on the meaning of it, which is why I'm having the problem. I think that the components of the alternating tensor look like \begin{bmatrix}
\epsilon_{111}A_{1,1} &\epsilon_{112}A_{1,2} &\epsilon_{113}A_{3,1} \\
\epsilon_{121}A_{1,2} &\epsilon_{122}A_{2,2}...