Following Example 7.18, identify the numbers that are half of every element in Z9. (That is, for each a ∈ Z9, find b ∈ Z9 such that 2b = a.) We talked extensively in this section about multiplicative...

Following Example 7.18, identify the numbers that are half of every element in Z9. (That is, for each a ∈ Z9, find b ∈ Z9 such that 2b = a.)

We talked extensively in this section about multiplicative inverses, but there can be inverses for other operations, too. The next few exercises explore the additive inverse in Zn. Notice that the additive identity in Zn is 0: for any a ∈ Zn, we have a + 0 ≡n 0 + a ≡n a. The additive inverse of a ∈ Zn is typically denoted −a.