Let a*b=a+ab for all `a,b in Q.` then

Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

Check the commutativity and associativity of * on Q defined by a*b=a+ab for all a,b in Q.

Let * : Q xx Q rarr Q be defined a as a * b = 1 + ab for all a, b in Q. Show that * is commutative but not associative.

Let ^(*) be a binary operation on set Q-[1] defined by a*b=a+b-ab for all a,b in Q-[1]. Find the identity element with respect to * on Q. Also,prove that every element of Q-[1] is invertible.

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}

The operation * on Q -(1) is define dby a*b = a+b - ab for all a,b in Q - (1) Then the identity element in Q -(1) is

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 every element of Q-{-1} is invertible.Also,find the inverse of an arbitrary element.

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

Let a mapping '*' from Q xx Q to Q (set of all rational numbers) be defined by a* b = a +2 b for all a, b in Q. Prove that * is a binary operation on Q