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}`

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

A binary operation * is defined on the set R of all real numbers by the rule a*b= sqrt(a^2+b^2) for all a ,\ b in R . Write the identity element for * on Rdot

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} .

If the binary operation o. is defined on the set Q^+ of all positive rational numbers by ao.b=(a b)/4dot Then, 3o.(1/5o.1/2) is equal to

The binary operation * is defined by a*b= (a b)/7 on the set Q of all rational numbers. Show that * is associative.

Write the identity element for the binary operations * on the set R_0 of all non-zero real numbers by the rule a * b=(a b)/2 for all a ,\ b in R_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.

The binary operation defined on the set z of all integers as a ** b = |a-b| - 1 is

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