Below is the solution to the inverse of a matrix in tensor notation, as a product of two permutation tensors. I'm confused about how the two permutations tensors interact with their associated A matrixes, any tips?

$A^{-1}_{ij} = {1 \over 2 \, \text{det} ({\bf A}) } \epsilon_{jmn} \, \epsilon_{ipq} A_{mp} A_{nq}$