Whenever we create the Levi-Civita image for a determinant like we did above, the fully antisymmetric assets that it possess results in being apparent: swapping any two indices corresponds to interchanging their corresponding rows in the matrix as a consequence of which the determinant, and that is the Levi-Civita itself, https://jaredeqdrb.bligblogging.com/27310580/getting-my-levis-4d-to-work