Final answer:
The student is asked to find the Cartesian product, not the cross product of vectors. The Cartesian product A x B consists of all possible ordered pairs with the first element from A and the second from B, and similarly for B x A with reversed order.
Step-by-step explanation:
The student is asking for the Cartesian product of two sets A and B, and not about the cross product of vectors, which is an algebraic operation discussed in vector analysis. The sets provided are A = {i, a} and B = {t, d, m}. The Cartesian product A x B is the set of all possible ordered pairs where the first element is from set A and the second is from set B. Conversely, B x A is the set of all possible ordered pairs where the first element is from set B and the second is from set A.
A x B = { (i, t), (i, d), (i, m), (a, t), (a, d), (a, m) }
B x A = { (t, i), (t, a), (d, i), (d, a), (m, i), (m, a) }
Each pair in the Cartesian product is unique and the order in which the elements appear in the pairs matters, hence the different results for A x B and B x A.