Prove that the contracted product of two tensors a. b, with components aikbk; is a tensor of order two. b. show that the doubly contracted product aįjbij of a symmetric tensor a and an antisymmetric tensor b vanishes c. show that a symmetric tensor remains symmetric under any transformation of axes d. given a tensor a and a vector b, prove that the contracted products a b and b · a are both vectors, that is show that aijb; and bịajj are components of vectors. note that they are not the same vector unless a is symmetric.