εⁱʲᵏεₖₗₘ = δⁱₖδʲₗ − δⁱₗδʲₖ
(since my mother told me to only sum over repeated indices when one is up and one is down). I sometimes compute with these things using Penrose's notation, which is really string diagrams in the symmetric monoidal category of vector spaces. He explained it in this paper:
https://www.mscs.dal.ca/%7Eselinger/papers/graphical-bib/public/Penrose-applications-of-negative-dimensional-tensors.pdf
