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 ?
I made the same mistake as you while first answering this.
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