# 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)   (Show Source): You can put this solution on YOUR website!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