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Show that the set {5, 15, 25, 35} is a group under

Chapter 2, Problem 16E

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QUESTION:

Show that the set {5, 15, 25, 35} is a group under multiplication modulo 40. What is the identity element of this group? Can you see any relationship between this group and U(8)?

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QUESTION:

Show that the set {5, 15, 25, 35} is a group under multiplication modulo 40. What is the identity element of this group? Can you see any relationship between this group and U(8)?

ANSWER:

Step 1 of 6

To prove that the set  is a group under multiplication module 40, we need to check that whether the set is closed under multiplication or not.

First multiply every number by 5 as:

                                                         

 

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