Dear All
Can I ask this question?
List all elements of the group Z8. For each element indicate its inverse?
Can I ask why Z8 has the element {1,3,5,7}
and 1^-1 = 1 and 3^-1 = 3, 5 ^-1 = 5, 7^-1 = 7?
Thanks a lot indeed.
Surely Z8 has the elements {0, 1, 2, 3, 4, 5, 6, 7}...
As for the inverses, draw up your additive and multiplicative tables, see which elements combine to give you 0 for the additive table and 1 for the multiplicative table, remembering that you will be doing modular arithmetic with base 8.