SOLUTION: Let * denote the binary operation defined on Q, the set of all rational numbers, by x*y=3xy, for all x, y in Q. Exactly which of the following properties does * have? i. Commutati

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Let * denote the binary operation defined on Q, the set of all rational numbers, by x*y=3xy, for all x, y in Q. Exactly which of the following properties does * have? i. Commutati      Log On


   



Question 856511: Let * denote the binary operation defined on Q, the set of all rational numbers, by x*y=3xy, for all x, y in Q. Exactly which of the following properties does * have?
i. Commutativity
ii. Associativity
iii. Has an identity

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Commutative:
x%2Ay=3xy
y%2Ax=3yx=3xy
So x%2Ay=y%2Ax.
It is commutative.
.
.
.
%28x%2Ay%29%2Az=3%28x%2Ay%29z=3%283xy%29%29z=9xyz
x%2A%28y%2Az%29=3x%28y%2Az%29=3x%283yz%29=9xyz
So %28x%2Ay%29%2Az=x%2A%28y%2Az%29
It is associative.
.
.
What exactly do you mean by identity for a two input operation?
Do you want x%2Ay=1???