Properties II For any rational number `a/b` we have `a/b -: 1 = a/b and a/b -: (-1)=- a/b = (-a)/b`

Properties III For every non-zero rational number (a)/(b) we have (i) (a)/(b)-:(a)/(b)=1 (ii) (a)/(b)-:(-(a)/(b))=-1 (iii) ((-a)/(b))-:(a)/(b)=-1

For all rational numbers a, b and c, a (b + c) = ab + bc.

For any two matrices A and B , we have

EXISTENCE OF RIGHT IDENTITY - The rational number 0 is the right identity.That is for any rational number (a)/(b) we have (a)/(b)-0=(a)/(b)

Commutativity : For any two literals a and b we have a+b=b+a

Let * be a binary operation on the set Q of rational numbers as follows: (i) a*b=a-b (ii) a*b=a^2+b^2 (iii) a*b=a+a b (iv) a*b=(a-b)^2 (v) a*b=(a b)/4 (vi) a*b=a b^2 Find which of the binary operations are commutative and which are associative