Whenever we publish the Levi-Civita symbol being a determinant like we did above, the thoroughly antisymmetric assets that it have turns into obvious: swapping any two indices corresponds to interchanging their corresponding rows from the matrix as a result of which the determinant, that's the Levi-Civita by itself, variations sign. https://levis4d56935.thezenweb.com/not-known-facts-about-levis-4d-64346365