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

I think no because the inverse of each of those elements is not in the set.....

Answer 2

for example, the inverse of 2 which is 1/2 in this case since binary operation is multiplication... and you can see well that 1/2 is not here

Answer 3

anonymous, it's modular multiplication, so inverses don't really work that way. However, I will agree that it's not a group, because it's not actually closed under multiplication, is it? 2*3 mod 6=0, for example.

Answer 4

but in this case there is no inverse for 2. correct me if I'm wrong :))
2*1=2 (mod6) 2*2=4 (mod6) 2*3=0 (mod 6)<btw this fact alone proves B. as nbouscal said
2*4=2 mod 6 2*5=4 mod 6

Answer 5

Right. I'm just saying you're going to confuse people if you say that the inverse of 2 is 1/2, because it isn't when you're doing modular multiplication :P But yes, the lack of inverse for 2 is another reason that it is not a group :)

Answer 6

@nbouscal my bad :))

Answer 7

can you help with my other math question please

Answer 8

Close this one and post a new one if you have a new question, please.

Answer 9

i did