Question

Decide whether or not the modulo system forms a group. {0, 1}; multiplication modulo 2

A. Group

B. Not a group

Answer 1

There are three properties a set with a operation must have to make a group.

1) The operation is associative

2) There is an identity element with respect to that operation

3) Every element must have an inverse with respect to the identity element.

Answer 2

So basically, ask yourself:

1) is multiplication associative?

2) Is there an abject in that set, call it e, where:\[a\cdot e=e\cdot a=a\] for all abjects a in the set?

3) Once youve found e, for all objects a in the set, is there another number b such that:\[a\cdot b = b\cdot a = e\]

Answer 3

so this is not a group

Answer 4

that is correct. For a couple of reasons. There is no proper identity element is one reason. Also, 0 doesnt have an inverse.

Answer 5

thanx

Answer 6

hmm..i take the second reason back, theres no point in talking about inverses if there isnt an identity.

Answer 7

but its still not a group right ?

Answer 8

that is right. with respect to multiplication it isnt a group. If we were talking about addition, then it would be.