1.Prove that the multiplicative inverse is unique: that is, for arbitrary n ≥ 2 and a ∈ Zn, suppose that ax ≡n 1 and ay ≡n 1. Prove that x ≡n y. 2. Write down the full multiplication table (as in...

1.Prove that the multiplicative inverse is unique: that is, for arbitrary n ≥ 2 and a ∈ Zn, suppose that ax ≡n 1 and ay ≡n 1. Prove that x ≡n y.

2. Write down the full multiplication table (as in Figure 7.17) for the following:

Figure 7.22: A reminder of two algorithms.