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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 `Adot` Find the invertible elements of `A` .

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Inverse
`a*x=e`
`(a,b)*(x, y)=(c, d)=(1, 0)`
`(ax, b+ay)=(1, 0)`
`ax=1` and `b+ay=0`
`x=1/a` and `y=-b/a`
Inversible `(1/a, -b/a)`
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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 A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)...

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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=Nuu{0}xxNuu{0} and let * be a binary operation on A defined 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=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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

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

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

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

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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 Q0 (set of non-zero rational numb...

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

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

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

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

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

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

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

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