## anilorap 3 years ago consider the binary operation * defined on Q* by a*b=3ab for all a,b in Q*. show (Q*,*) is abelian

1. experimentX

a*b = 3ab = 3ba = b*a

2. anilorap

can u do that?

3. experimentX

of course multiplication of numbers in commutative

4. anilorap

mmmmm interesting detail.. i didnt know i can apply that

5. experimentX

also you have to show Q is a group

6. anilorap

ohhh for real.....

7. matricked

closure for all a,b belongs to Q a*b=3ab belongs to Q thus closure property is satisfied associativity (a*b)*c=(3ab)*c=9abc again a*(b*c) =9abc thus associative property satisfied identity let i be the identity elemnt then i*a=a or 3ai=a or i=1/3 (for all not0) and belongs to Q inverse let x be the inverse of a if possible then a*x=1/3 or x=1/(3a) (for all a not 0) and the inverse exist in Q*(as Q*=Q-{0}) now a*b=3ab=3ba=b*a thes commutative property is satisfied hence (Q*,*) is an abelian group

8. anilorap

i did associative, right before u posted... omgg... i though it was easier