help with a group question please

[mathsfun]

can somebody pls help with the following:

Let G={1, -1,i,-i} where i^2 = -1. Show that G is an abelian group and give the group table.

[bloodhound]

form a group table under multiplication

1 -1 i -i
1 1 -1 i -i
-1 -1 1 -i i
i i -i -1 1
-i -i i 1 -1



and just look at the elements of G times G. u can see that ab =ba whenever a,b in G

[mathsfun]

thanks

[matt grime]

It's a finite subset sof the complex numbers closed under multiplication and possessing inverses and identity, hence it is an abelian group. They really asked you to write out the group table? What level course is this?

[bloodhound]

probably first year maths. i had to do that sort of stuff in my "Groups for Dummies"

[Dogtanian]

They really asked you to write out the group table? What level course is this?
In my semigroups course I had a question the other week where I had to draw the multiplication table for the semigroup of just 2 elements...I guess at all levels there can be some need to use the tables of the simplest groups etc.

[Aeschylus]

It's when they make you draw the multplictaion table for the trivial group that you should rise up and overthrow your maths teachers.

[mathsfun]

It's a finite subset sof the complex numbers closed under multiplication and possessing inverses and identity, hence it is an abelian group. They really asked you to write out the group table? What level course is this?

this is a 1st year course, although to me it seems so difficult

[matt grime]

It's not about the difficulty, it's a query about utility. Writing out group tables doesn't really help you do anything that you're not better off doing without them you see.

If you have to use tables, have you heard of the latin square principle?