Question

Decide whether or not the modulo system forms a group.{1, 2, 3, 4, 5}; multiplication modulo 6
A. Group

B. Not a group

Answer 1

the operation is multiplication right? not addition

Answer 2

then it fails to be a group
and the reason is, not every element has an inverse

Answer 3

the identity under multiplication is 1 and you cannot for example solve
\[2\times a=1\] for any element of the group. try it

Answer 4

is it clear why that doesn't work?