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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify which of the following elements are invertible in ℤ₄: 0, 1, 2, 3.
💡 Hint: Check which elements can yield 1 when multiplied.
Question 2
Easy
What is the definition of an invertible element?
💡 Hint: Think about the conditions for obtaining the multiplicative identity.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Which of the following elements is not invertible in ℤ₄?
- 0
- 1
- 3
- 2
💡 Hint: Check each element by determining its products.
Question 2
True or False: All elements of a field have inverses under multiplication.
- True
- False
💡 Hint: Recall the definition of a field.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a ring ℤ₈, determine the set of all invertible elements and provide justification for each element's inclusion or exclusion.
💡 Hint: Use the GCD method to evaluate each element.
Question 2
Explain why the presence of the multiplicative identity (1) and the closure property are essential for U(ℝ) to form a group.
💡 Hint: Reflect on the definition of group axioms.
Challenge and get performance evaluation