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Let * be a binary operation on Q0 (se...

Let * be a binary operation on `Q_0` (set of non-zero rational numbers) defined by `a*b=(3a b)/5` for all `a ,\ b in Q_0` . Show that * is commutative as well as associative. Also, find the identity element, if it exists.

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Commutative
`a * b = (3ab)/5`
`b *a = (3ba)/5 = 3ab/5`
` ⇒ a * b = b * a`
Hence `*` is commutative

Associative
`a*(b*c)=a*(3bc/5)=(9abc/25)` ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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

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

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

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

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

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

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

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

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

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  11. Let * be the binary operation on N defined by a*b=H C F of a and b ...

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  12. Consider the set S={1,\ -1} of square roots of unity and multiplica...

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  13. Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity...

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  14. Consider the set S={1,\ -1,\ i ,\ -i} of fourth roots of unity. Con...

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  15. Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on...

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  16. \begin{tabular}{|l|l|l|l|l|l|} \hline 1 & 1 & 2 & 3 & 4 & 5 \\ \hline ...

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  17. Consider a binary operation * on the set {1, 2, 3, 4, 5} given by t...

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  18. Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as...

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  19. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

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  20. Define a binary operation * on the set A={1,\ 2,\ 3,4} as a*b=a b\ ...

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