When we write the Levi-Civita image as being a determinant like we did higher than, the fully antisymmetric home that it have gets to be obvious: swapping any two indices corresponds to interchanging their corresponding rows inside the matrix due to which the determinant, and that is the Levi-Civita itself, https://levis4d25703.shotblogs.com/levis-4d-for-dummies-40605487