Let * be a binary operation on `Q-{-1}` defined by `a`*`b=a+b+a b` for all `a ,\ b in Q-{-1}` . Then, Show that * is both commutative and associative on `Q-{-1}` . (ii) Find the identity element in `Q-{-1}`

Let * be a binary operation on Q-{-1} defined by a*b=a+b+ab for all a,b in Q-{-1}. Then,Show that * is both commutative and associative on Q-{-1} (ii) Find the identity element in Q-{-1}

Let * be a binary operation on the set Q_0 of all non-zero rational numbers defined by a*b= (a b)/2 , for all a ,\ b in Q_0 . Show that (i) * is both commutative and associative (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all a ,\ b in Q-{0} . Prove that * is commutative on Q-{0} .

Let 'o' be a binary operation on the set Q_0 of all non-zero rational numbers defined by a\ o\ b=(a b)/2 , for all a ,\ b in Q_0 . Show that 'o' is both commutative and associate (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

Let ^(*) be a binary operation on Q-{0} defined by a*b=(ab)/(2) for all a,b in Q-{0} Prove that * is commutative on Q-{0}

Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,b in Q ,find identity element in Q

Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for all a ,\ b in Q-{-1} . Then, Show that every element of Q-{-1} is invertible. Also, find the inverse of an arbitrary element.

Let * be a binary operation on Q_0 (set of non-zero rational numbers) defined by a*b= (3a b)/5 for all a ,\ b in Q_0 . Show that * is commutative as well as associative. Also, find the identity element, if it exists.

Let * be a binary operation o Q defined by a^(*)b=(ab)/(4) for all a,b in Q,find identity element in Q