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

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ . Find the identity element in (Z,*)

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---

On the set Q^+ of all positive rational numbers if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in Q^+ .

On the set QQ^(+) of all positive rational numbers if the binary operation ** is defined by a**b=(1)/(4)ab for all a,binQQ^(+) , find the identity element in QQ^(+) . Also prove that any element in QQ^(+) is invertible.

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

Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on A by a@b=ab(mod6) for all a,bin A. Find the identity element for @ in A . Show that 1 and 5 are the only invetible elements in A.

A binary operation ** is defined in QQ_(0) , the set of all non-zero rational numbers, by a**b=(ab)/(3) for all a,binQQ_(0) . Find the identity element in QQ_(0) . Also find the inverse of an element x in QQ_(0) .

A binary operation @ is defined on RR-{-1} by a@b=a+b+ab for all a,binRR-{-1}. (i) Discuss the commutativity and associativity of @ on RR-{-1} . Find the identity element, if exists. (iii) Prove that every element of RR-{-1} is invertible.

*' is an operation defined on Z set of all integers as a*b = a+b-2 for all a,b in z . Find identity element of *'