The inverse of the multiplication module 13 is: The two values are multiplied with modul 13. The inverse is the rest of the division when the division it's iqual to 1, because 1 it's a neutral element of the multiplication. Example: 6 mod 13 = 6 because 6 it's the rest of division. 11 mod 13 = 11 But (6*11)mod13 = 66 mod(13) = 1. The inverse of the 6 it's 11 because mod(6 mod 13 * 11 mod 13) = 1 Zero has no inverse because it is not an element of the list.