BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS

FURTHER MATHEMATICS SSS1 FIRST TERM                   

WEEK 8

BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS

Contents

Identity element and Inverse element

Identity Element:

     Given a non-empty set S which is closed under a binary operation * and if there exists an element e € S such that a*e = e*a = a for all a € S, then e is called the IDENTITY or NEUTRAL element. The element is unique.

Example: The operation * on the set R of real numbers is defined by a*b = 2a-1 ┼ b

                                                                                                                          2

for all a, b € R. Determine the identity element.

Solution:

      a*e= e*a = a

      a*b= 2a-1 ┼ b

                 2

     a*e = 2a-1 ┼ e =…