Does the operation * defined below on the given set represent a binary operation? : `a**b=ab` on `Z^+`

Does the operation * defined below on the given set represent a binary operation? : a**b=a-b on Z^+

Does the operation * defined below on the given set represent a binary operation? : a**b=a+4b^2 on R

Does the operation * defined below on the given set represent a binary operation? : a**b=(a+b)/2 on N

Let ** on the set integers I be a binary operation defined by a**b=3a+4b-2 . Find 4**5 .

Is the binary operation ** defined on the set of integer Z by the rule a**b=a-b+2 commutative ?

Let ** be a binary operatiion defined by a**b=3a+4b-2 .Find 4**5 ?

Is the binary operation ** defined on the set of rational numbers by the rule a**b=ab//4 associative ?

Let * be a binary operation defined by a*b = 3a+4b-2 find 4*5

For the binary operation ** defined below, determine whether ** is commutative and associative : On Z, define a**b=ab+1

Show that the operation * defined on Q-{1} by a**b=a+b-ab is abinary operation. Is * commutative and associative? What is the identity element wrt *? Which elements possess inverses?