Question

Consider the set G= {1,5,7,11,13,17} under multiplication modulo 18 as a group. Construct the multiplication table for G and find the inverse of each element of G.

Answer 1

x18	1	5	7	11	13	17
1	1	5	7	11	13	17
5	5	7	17	1	11	13
7	7	17	13	5	1	11
11	11	1	5	13	17	7
13	13	11	1	17	7	5
17	17	13	11	7	5	1

Inverse of element 1 under x₅ (multiplication modulo 18) = 1

Inverse of element 5 = 1

Inverse of element 7 = 13

Inverse of element 11 = 5

Inverse of element 13 = 7

Inverse of element 17 = 17