For the binary operation * defined on `R-{-1}` by the rule `a`*`b=a+b+a b` for all `a ,\ b in R-{1}`, the inverse of `a` is

For the binary operation * defined on R-{-1} by the rule a*b=a+b+ab for all a,b in R-{1}, the inverse of a is a (b) -(a)/(a+1)(c)(1)/(a) (d) a^(2)

Consider the binary operation * defined on Q-{1} by the rule a*b= a+b-a b for all a ,\ b in Q-{1} . The identity element in Q-{1} is (a) 0 (b) 1 (c) 1/2 (d) -1

Consider the binary operation * defined on Q-{1} by the rule a*b=a+b-a b for all a ,\ b in Q-{1} . The identity element in Q-{1} is (a) 0 (b) 1 (c) 1/2 (d) -1

Let * be a binary operation defined on Q^+ by the rule a * b=(a b)/3 for all a ,\ b in Q^+ . The inverse of 4 * 6 is (a) 9/8 (b) 2/3 (c) 3/2 (d) none of these

Let * be a binary operation defined on Q^+ by the rule a*b=(a b)/3 for all a , b in Q^+ . The inverse of 4*6 is 9/8 (b) 2/3 (c) 3/2 (d) none of these

Is the binary operation ** defined on Z (set of integers) by the rule a**b=a-b+ab for all a, bin Z commutative ?

Let '*' be the binary operation defined on Q by the rule a * b = (ab)/(4) for all a , b in Q . Is the operaiton * associative?

Let '*' be the binary operation defined on Q by the rule a * b = ab^2 for a , b in Q. compute (1*2) *3.

Q^+ is the set of all positive rational numbers with the binary operation * defined by a*b= (a b)/2 for all a ,\ b in Q^+ . The inverse of an element a in Q^+ is a (b) 1/a (c) 2/a (d) 4/a