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## MTH405 Assignment 1 Spring 2023 – Assignments – Solution VU

**Assignment No. 1 MTH405 (Spring 2023)**

**Total Marks: 15 ****Due Date: ****May 28, 2023**

**DON’T MISS THESE****: Important instructions ****before attempting the solution of this assignment:**

**To solve this assignment, you should have good command over 1-10 lectures.****Upload assignments properly through LMS, No Assignment will be accepted through email.****Write your ID on the top of your solution file.**

**Don’t use colorful back grounds in your solution files.****Use Math Type or Equation Editor etc. for mathematical symbols if needed.****You should remember that if the solution files of some students are found same (copied) then we will reward zero marks to all those students****.****Make solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks.****Also remember that you are supposed to submit your assignment in****Word format****. Any other format like scanned images etc. will not be accepted and be awarded zero marks**

**Q1** Show that the inverse of each element of a group G is unique. Marks = 6

**Q2:** Find the order of each element of the group 1, -1, i, -i. Marks = 6

**Q3:** Give an example of a group which is abelian but not cyclic. . Marks = 3

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