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For the binary operation `ast` defined on `R-{-1}` by the rule `a ast b=a+b+a b` for all `a ,\ b in R-{1}`, the inverse of `a` is

A

(a) `a`

B

(b) `-a/(a+1)`

C

(c) `1/a`

D

(d) `a^2`

Text Solution

Verified by Experts

The correct Answer is:
(b) `-a/(a+1)`
For inverse
`aoa^-1=a^-1oa=e` `a forall R`

For identity `e`
`aoe=eoa=a``a forall R`
`a ast e=a`
`a+e+ae=a`
`e(1+a)=0`
`e=0`

...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. If the binary operation o. is defined on the set Q^+ of all positive r...

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  3. Let * be a binary operation defined on set Q-{1} by the rule a*b=a+b...

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  4. Which of the following is true? * defined by a*b=(a+b)/2 is a binar...

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  6. If a binary operation * is defined by a*b=a^2+b^2+a b+1 , then (2*3...

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  7. Let * be a binary operation on R defined by a*b=a b+1 . Then, * is ...

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  8. Subtraction of integers is

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  9. The law a+b=b+a is called

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  10. An operation * is defined on the set Z of non-zero integers by a*b=a/...

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  11. On Z an operation * is defined by a * b=a^2+b^2 for all a ,\ b in Z...

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  12. A binary operation ast on Z defined by a ast b=3a+b for all a ,\ b i...

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  14. Consider the binary operation ast defined on Q-{1} by the rule a ast...

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  15. For the binary operation ast defined on R-{-1} by the rule a ast b=a...

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  16. For the multiplication of matrices as a binary operation on the set ...

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  17. On the set Q^+ of all positive rational numbers a binary operation *...

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  18. Let ast be a binary operation defined on Q^+ by the rule a ast b=(a...

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  19. The number of binary operations that can be defined on a set of 2 el...

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  20. The number of commutative binary operations that can be defined on a...

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