How to Make a Cayley Table


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question 1 of 3

Given the Cayley Table of the BINGO group below, what is the inverse of the element G?

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1. The Klein Four Group is a well-known example of a group. Given its Cayley Table below, what is the identity element?

2. Which of these tables could be a correct Cayley Table for a group consisting of the elements x, y, and z?

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About This Quiz & Worksheet

This quiz and worksheet is designed to help you test how well you understand the processes involved in making a Cayley Table. Our quiz will ask you about the characteristics from a variety of example Cayley Tables, as well as their properties and elements.

Quiz & Worksheet Goals

When you take this quiz, you'll be asked to:

  • Identify the inverse of an element in an example Cayley Table
  • Detail the identity element from an example Klein Four Group
  • Select the correct Cayley Table matching a given group of elements
  • Explain the components of a Cayley Table for the group of symmetries of a non-square rectangle
  • Determine why an example table could not be a Cayley Table

Skills Practiced

  • Knowledge application - use your knowledge to answer questions about finding the inverse of an element in an example Cayley Table
  • Reading comprehension - ensure that you draw the most important information from the related Cayley Table lesson
  • Information recall - access the knowledge you've gained regarding the characteristics of Cayley Tables

Additional Learning

Study more about this interesting topic using our lesson called How to Make a Cayley Table. Once you complete this lesson, you should understand how to:

  • Explain what it means if a Cayley Table is an order 3
  • Describe the type of group for which a Cayley Table is designed
  • Detail uses of Cayley Tables