Let * be a binary operation on `Z` defined by a*b= `a+b-4` for all `a ,\ b in Zdot` Show that * is both commutative and associative.

Let * be a binary operation on Q-{-1} defined by a * b=a+b+a b for all a ,\ b in Q-{-1} . Then, Show that * is both commutative and associative on Q-{-1} . (ii) Find the identity element in Q-{-1}

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=a for all a ,\ b in Adot Is * commutative or associative on A ?

Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all a ,\ b in Q-{0} . Prove that * is commutative on Q-{0} .

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in Adot Is * commutative or associative on A?

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in Adot Is * commutative or associative on A?

Let * be a binary operation on the set Q_0 of all non-zero rational numbers defined by a*b= (a b)/2 , for all a ,\ b in Q_0 . Show that (i) * is both commutative and associative (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

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

Let A be a set having more than one element. Let '*' be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in A . Is '*' commutative or associative on A?

Let A = R × R and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Show that * is commutative and associative. Find the identity element for * on A.

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.