Let * be an associative binary operation on a set S with the identity element e in S. Then. the inverse of an invertible element is unique.

A binary operation on a set has always the identity element.

A binary operation on a set has always the identity element.

A binary operation on a set has always the identity element.

Let * be an associative binary operation on a set S and a be an invertible element of S. Then; inverse of a^(^^)-1 is a.

Define an associative binary operation on a non-empty set S.

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. Find the identity element in Z .(ii) Find the invertible elements in Z .

Definition and Theorem: Let * be a binary operation on a set S.If S has an identity element for * then it is unique.

The total number of binary operations on the set S={1,2} having 1 as the identity element is n . Find n .

Let A = R xx R and * be a 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. Also find the inverse of every element (a,b) in A.