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Show that the binary operation * on A=R-...

Show that the binary operation * on `A=R-{-1}` defined as `a*b=a+b+a b` for all `a ,bA` is commutative and associative on `Adot` Also find the identity element of `*` in `A` and prove that every element of A is invertible.

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. On Q, the set of all rational numbers, a binary operation * is defined...

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  2. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

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  3. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

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  4. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  5. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  6. Let * be a binary operation on N given by a*b=LdotCdotM(a ,\ b) for ...

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  7. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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  8. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

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  9. On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity ...

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  10. Let X be a non-empty set and let * be a binary operation on P(X) (t...

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  11. Let X be a nonempty set and *be a binary operation on P(X), the power ...

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  12. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

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  13. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

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  14. Let A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)...

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  15. Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)...

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  16. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by...

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  17. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

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  18. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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  19. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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  20. Show that the number of binary operations on {1," "2} having 1 as iden...

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