Prove that the operation `@` on `QQ`, the set of rational numbers, defined by `a@b=ab+1` is binary operational on `QQ`.

Is @ defined on QQ the set of rational numbers, by a@b=(a-1)/(b-1)(a,binQQ), a binary operation?

The operation ** defined by a ** b =(ab)/7 is not a binary operation on

Prove that the operation * on the set M={[a0 0b]: a ,\ b in R-{0}} defined by A*B=A B is a binary operation.

Prove that the operation 'addition' on the set of irrational numbers is not a binary operation.

Let @ be a binary operation on QQ , the set of rational numbers, defined by a@b=(1)/(8)ab for all a,binQQ . Prove that @ is commutive as well as associative.

Prove that the operation * on the set M={[a00b]:a,b in R-{0}} defined by A*B=AB is a binary operation.

Define a binary operation on a set.

Define a binary operation on a set.

On the set Q of all rational numbers an operation * is defined by a*b=1+ab. show that * is a binary operation on Q.