Let (R 3 , ×) be the set of 3d vectors equipped with theoperation of vector crossproduct. Which of the following propertiesdoes this operation satisfy (give proofs in all cases)?
(a) has identity element(s)? (If so, determine all identityelements.)
(b) has idempotent element(s)? (If so, determine all idempotentelements.)
(c) commutative?
(d) associative?
