If the operation * is defined on the set `Q` of all rational numbers by the rule `a*b=(a b)/3` for all `a ,\ b in Q` . Show that * is associative on `Qdot`

If the operation * is defined on the set Q of all rational numbers by the rule a*b=(ab)/(3) for all a,b in Q. Show that * is associative on Q

If the operation * is defined on the set Q - {0} of all rational numbers by the rule a * b=(a b)/4 for all a ,\ b in Q - {0} . Show that * is commutative on Qdot - {0}

Is the binary operation ** defined on the set of rational numbers by the rule a**b=ab//4 associative ?

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule a*b= (3a b)/7 for all a ,\ b in Rdot

On Q , the set of all rational numbers a binary operation * is defined by a*b= (a+b)/2 . Show that * is not associative on Qdot

On the set Q of all rational numbers if a binary operation * is defined by a*b= (a b)/5 , prove that * is associative on Qdot

On Q, the set of all rational numbers a binary operation * is defined by a*b=(a+b)/(2) Show that * is not associative on Q.

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 (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.