Exercise 5. 1. Write out the multiplication table for the integers modulo 6 2. Write down the multiplicative inverses for the integers modulo 6. Be sure to represent each multiplicative inverse by an integer in {0,1,2, 3,4,5 3. Notice that not all of the integers modulo 6 have multiplicative inverses. Which ones do not? 4. Write down the pairs of integers modulo 6 which equal [O] when multiplied together. Exercise 6. Let n E Z. Prove that for all z, y, z Z, if x y (mod n), then zz-yz (mod n)