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 ^(*) 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 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 Q, defined by a * b =(ab)/(2), AA a,b in Q . Determine whether * is commutative or associative.

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 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_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.

Check the commutativity of * on Q defined by a*b=(a-b)^2 for all a ,\ b in Q .

Check the commutativity of * on Q defined by a*b=a b^2 for all a ,\ b in Q .