# 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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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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Step 1

Calculation:

Obtain the Cayley table for the set S = {5,15,25,35} under the multiplication modulo 40 as follows.

Step 2

The above table is observed to contain all the elements of the set S. So, ×40 is closed and associative.

From the Cayley table the following observations are made.

• The identity element is observed to be 25, since x ×40 25 = x,  ∈ S
• The inverse of 5 is ...

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