13.2 - Group Axioms
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the first axiom of a group?
💡 Hint: Consider what happens when you combine two numbers from the set.
Is zero the identity element in the group of integers under addition?
💡 Hint: Think about adding zero to any number.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the closure property entail?
💡 Hint: Think about the results of combining elements from a set.
True or False: An identity element must be unique within a group.
💡 Hint: Consider the implications of having multiple identity elements.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Consider the set of all integers. Prove whether it forms a group under subtraction.
💡 Hint: Think about operations and how subtraction behaves compared to addition.
Given a set of matrices with a defined matrix addition, explain whether it can form a group and why.
💡 Hint: Do matrices behave like numbers in terms of addition?
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.