Determine whether * is commutative or associative if `a**b=(ab)/6,a,bnotinR`

For each binary operation ** defined below, determine whether ** is commutative or associative on Q, define a**b=2^(ab)

For each binary operation ** defined below, determine whether ** is commutative or associative on Z, define a**b=a-b

For each binary operation ** defined below, determine whether ** is commutative or associative on Q, define a**b=ab+1

For each binary operation ** defined below, determine whether ** is commutative or associative on Z^+ , define a**b=a^b

For each binary operation ** defined below, determine whether ** is commutative or associative on R-{-1} , define a**b=a/(b+1)

ast ' is a binary operation on R defined as aastb=2ab Determine whether ast is commutative and associative

Check whether the following binary operation on the set R are associative and commutative. a ** b=((a+b))/2AAa,b in R

Let ** be a binary operation on the set Q of rational numbers as follows a**b=a-b . Check whether * is commutative and associative

Let ast be a binary operation on the set Q of rational numbers defined by aastb=frac(ab)(3) . Check whether ast is commutative and associative?

Let ' ast ' is a binary operation on the set Q of rational numbers as follows, aastb=a+ab Check whether the binary operation are commutative and associative. Also find the identify element if exists.