four vectors

Thought it would be wise to recall some of the concepts before proceeding further.So,I started with revising the section on Four Vectors of sec 6 of Landau-Lifshitz(LL).
there is one thing i wanted to clarify.A quantity that is a product of a pseudoscalar and a scalar is a pseudoscalar; the product of a pseudoscalar with another pseudoscalar would be a scalar.I can extend the same argument to vectors and tensors; and then i would claim that (levi-civita_iklm)*(levi-civita_prst) is a true tensor.