Q. Let * be the binary operation on the rational no. given by a*b = a+b+2ab, which is true ?
I * is commutative
II There is a rational no that is a *  identity
III Every rational no has a *  inverse
A) I only
B) II only
C) I , II only
D) I and III only
E) I II and III
I thought ans is E, but ans is C, can somebody explain ?
GR8767 Q17

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 Joined: Mon Mar 22, 2010 2:42 am
Re: GR8767 Q17
I made the same mistake as you while first answering this.mathQ wrote:Q. Let * be the binary operation on the rational no. given by a*b = a+b+2ab, which is true ?
I * is commutative
II There is a rational no that is a *  identity
III Every rational no has a *  inverse
A) I only
B) II only
C) I , II only
D) I and III only
E) I II and III
I thought ans is E, but ans is C, can somebody explain ?
If III is correct we could suppose that the inverse is a^1, therefore we have a+a^1+2aa^1=0
from which we could obtain a^1=1/(2a+1)
and we could clearly know that the inverse does not exist while a=1/2