When we publish the Levi-Civita image to be a determinant like we did above, the totally antisymmetric property that it have results in being evident: swapping any two indices corresponds to interchanging their corresponding rows within the matrix as a consequence of which the determinant, that's the Levi-Civita itself, improvements https://levis4d25914.blogoscience.com/32645539/the-basic-principles-of-levis-4d