Example Question #1 : Groups
Which of the following is an identity element of the binary operation ?
Defining the binary operation will help in understanding the identity element. Say is a set and the binary operator is defined as for all given pairs in .
Then there exists an identity element in such that given,
Therefore, looking at the possible answer selections the correct answer is,
Example Question #2 : Abstract Algebra
Which of the following illustrates the inverse element?
For every element in a set, there exists another element that when they are multiplied together results in the identity element.
In mathematical terms this is stated as follows.
For every such that where and is an identity element.