Find the identity element of (Q,*)? If (Q,*) is map to (Q,X) given by map(x)=3x-1 is group homorphism, where the binary operation in (Q,*) is a*b=3ab-a-b+2/3.

Hint: when the binary operation is a*b=1/3(ab-a-b+2). The identity element is 2.

Question

Find the identity element of (Q,*)? If (Q,*) is map to (Q,X) given by map(x)=3x-1 is group homorphism, where the binary operation in (Q,*) is a*b=3ab-a-b+2/3.

Hint: when the binary operation is a*b=1/3(ab-a-b+2). The identity element is 2.

anonymous · Answer

i guess after teasing out all this weird verbiage, what you are being asked to do is find the inverse image of 2

anonymous · Answer

since the identity must go to the identity and vice versa

anonymous · Answer

no 2 is the answer for another question
however i not sure of the working for either one

anonymous · Answer

oh ok. i am not sure what all that other business is about then, the homomphism etc

anonymous · Answer

i think you find this as follows 
you know $a*e=a$ because $e$ is the identity, and 
$$a*e=3ae-a-e+\frac{2}{3}$$by definition of $*$ so set them equal and solve for $e$

anonymous · Answer

you get 
$$a=3ae-a-e+\frac{2}{3}$$ or 
$$2a=3ae-e+\frac{2}{3}$$ telling you $e=\frac{2}{3}$