On Q defined * by `a ** b = ab + 1` show that * commutative.

Let '*' be a binary operation on Q defined by a * b = (3ab)/5. Show that * is commutative as well as associative. Also, find its identity element, if it exists.

Let '*' be a binary operation on Q defined by : a* b = (3ab)/5 . Show that * is commutative as well as associative. Also find its identity element, if its exists.

On Q define * by a ** b = (ab)/3 . Show that * is associative.

On Q, define * by a ** b = (ab)/4 . Show that * is both commutative and associative.

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

Let* be a binary operation on Q, defined by a*b= (3ab)/(5) .Show that is commutative as well as associative. Also, find its identity, if it exists.

Let * be a Binary operation defined on N by a ** b = 2^(ab) . Prove that * is commutative.

A binary operation ** be defined on the set R by a**b = a+b +ab . Show that ** is commutative, and it is also Associative.

Show that * : R × RrarrR defined by a * b = a + 2b is not commutative.

Show that **: R × R to R defined by a **b=a + 2b is not commutative.