SOLUTION: 1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *.

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Question 93182: 1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *.

Answer by venugopalramana(3286) About Me  (Show Source):
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1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *.
LET I BE THE IDENTITY ELEMENT WRT * OPERATION.SO
A*I=A=A+I+AI
I(A+1)=0
I=0
HENCE IF X IS INVERSE OF A THEN
A*X=I=0=A+X+AX
X(A+1)= -A
X=-A/(A+1)
HENCE A SHOULD NOT BE -1
SO ALL ELEMENTS IN R EXCEPT A=-1 ARE INVERTIBLE