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Let A=QxxQ and let ** be a binary oper...

Let `A=QxxQ` and let `**` be a binary operation on `A` defined by `(a ,\ b)*(c ,\ d)=(a c ,\ b+a d)` for `(a ,\ b),\ (c ,\ d) in A` . Then, with respect to `**` on `A`. Find the identity element in `A`.

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`A=Q×Q`
`(a,b),(c,d) in A`, ∗ is defined by `(a,b)∗(c,d)=(ac,b+ad)`
To check `(a,b)∗(c,d)=(c,d)∗(a,b)` for any `(a,b),(c,d) in A`
Now, `(a,b)∗(c,d)=(ac,b+ad) `
`(c,d)∗(a,b)=(ca,d+cb)=(ac,d+bc) ! =(ac,b+ad)` ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

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

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

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

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

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

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

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

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

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  10. Determine the total number of binary operations on the set S={1,\ 2...

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  11. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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  12. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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

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  14. Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for all...

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  15. Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for al...

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  16. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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  17. Let 'o' be a binary operation on the set Q0 of all non-zero rati...

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  18. On R-[1] , a binary operation * is defined by a*b=a+b-a b . Prove that...

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  19. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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  20. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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