A binary operation `@` on `QQ-{1}` is defined by `a**b=a+b-ab` for all `a,binQQ-{1}.` Prove that every element of `QQ-{1}` is invertible.

An operation @ on QQ-{-1} is defined by a@b=a+b+ab for a,binQQ-{-1}. Find the identity element einQQ-{-1} .

A binary operation ** on QQ_(0) , the set of all non-zero rational numbers, is defined as a**b=(1)/(3)ab for all a,binQQ_(0) Prove that every element of QQ_(0) , is invertible and find the inverse of the element (3)/(5)inQQ_(0).

The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN is--

Let ** be a binary operation on set QQ-{1} defined by a**b=a+b-abinQQ-{1}. e is the identity element with respect to ** on QQ . Every element of QQ-{1} is invertible, then value of e and inverse of an element a are---

The binary operation * define on N by a*b = a+b+ab for all a,binN is

(I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. (ii) let ** be a binary operation on RR-{-1} , defined by a**b=(1)/(b+1) for all a,binRR-{-1} Show that ** is neither commutative nor associative. (iii) Let ** be a binary operation on the set QQ of all raional numbers, defined as a**b=(2a-b^(2)) for all a,binQQ . Find 3**5 and 5**3 . Is 3**5=5**3?

Let * be a binary operations on Z and is defined by , a * b = a + b + 1, a, bin Z . Find the identity element.

Prove that the operation ** on ZZ defined by a**b=a|b| for all a,binZZ is a binary operation

Prove that the binary operation ** on RR defined by a**b=a+b+ab for all a,binRR is commutative and associative.

Let be binary operation on the set R defined by a*b = a+b+ab, a, binR . solve equation :2*(2*x)=7