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Let '*' be a binary operation on Q0 (set...

Let `'*'` be a binary operation on `Q_0` (set of all non-zero rational numbers) defined by `a*b=(a b)/4` for all `a , b in Q_0dot` Then, find the identity element in `Q_0` inverse of an element in `Q_0dot`

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For` {a}, {b} in {Q} * `is a binary operation on` {Q} as {a} * {~b}=frac{3 {ab}}{5}`
Now `b * a=frac{3 b a}{5}`
As `a b=b a`
`Rightarrow frac{3 a b}{5}=frac{3 b a}{5} `
therefore `a * b=b * a`
So, the binary operation * is commutative.
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  12. Let * be a binary operation on N, the set of natural numbers, defined ...

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  13. Let *, be a binary operation on N, the set of natural numbers defined ...

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  14. On Q, the set of all rational numbers, a binary operation * is defined...

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  16. On the set C of all complex numbers an operation 'o' is defined by ...

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  17. Let S={1,2,3,4} and * be an operation on S defined by a*b=r , where r ...

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