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 on Q defind by a*b= (ab)/(2), AA a,b in Q Determine whether * is associative or not.

Let * be a binary operation on Q defined by a**b=ab+1 . Determine whether * is commutative but not associative.

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 defined by : a**b=(2ab)/(3) . Show that '**' is commutative as well as associative.

If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R . Then the operation ** is (i) Commutative but not associative. (ii) Associative but not commutative . (iii) Neither commutative nor associative . (iv) Both commutative and associative.

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}

* be a binary operation on Q,defined as a**b=(3ab)/5 .Show that *is commutative.

For each binary operation ** defined below, determine whether ** is commutative or associative on Q, define a**b=2^(ab)