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Let * be a binary operation on set Q-[1]...

Let * be a binary operation on set `Q-[1]` defined by `a*b=a+b-a b` for all`a , b in Q-[1]dot` Find the identity element with respect to `*onQdot` Also, prove that every element of `Q-[1]` is invertible.

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Verified by Experts

Let `e` is the identity element for the given operation.
Then, `a**e = a`
`=>a+e-ae = a`
`=> e(1-a) = 0`
`=> e = 0 and a = 1`
It is given that `Q` does not contain `1`.
`:. a` can not be `1`.
`:. e = 0`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  16. If * is defined on the set R of all real numbers by a*b=sqrt(a^2+b^2) ...

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  17. If the binary operation * on the set Z is defined by a*b=a+b-5, then ...

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  18. Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,bin Q...

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  19. If the binary operation o. is defined on the set Q^+ of all positive r...

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