1. The problem statement, all variables and given/known data 1.) Prove that the infinitesimal volume element d3x is a scalar 2.) Let Aijk be a totally antisymmetric tensor. Prove that it transforms as a scalar. 2. Relevant equations 3. The attempt at a solution 1.) Rkh = ∂x'h/∂xk By coordinate transformation, x'h = Rkh xk dx'h = (∂x'h/∂xk) (∂xk/∂x'j) (∂x'i/∂xj) dxj dx'h = δih Rji dxj dx'h = Rjh dxj This shows that the differential doesn't affect the transformation hence by performing the differential three times it would not affect the transformation, that is, it is a scalar. Can anyone verify if this is correct? 2.) A'mnl = ( T'mnl - T'lnm ) = RimRjnRklTmnl - RklRjnRimTlnm = RimRjnRkl(Tmnl - Tlnm) What should I do next here?