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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem

Let S be a set of three elements given by S = { A , B , C } . In the following table, all of the elements of S are listed in a row at the top and in a column at the left. The result x y is found in the row that starts with x at the left and in the column that has y at the top. For example, B C = C and C B = A . Thus the table defines the binary operation on the sets S .

A B C
A A B C
B B C A
C C A B

a. Is the binary operation commutative? Why?

b. Determine whether there is an identity element in S for .

c. If there is an identity element, which elements have inverses?

a)

To determine

Whether the given binary operation is commutative.

Explanation

Given Information:

The set S={A,B,C} is given and the table that defines the binary operation on the set S is given as:

A B C
A A B C
B B C A
C C A B

Explanation:

Consider the given table

b)

To determine

Whether there is an identity element in S.

c)

To determine

The inverse of elements of S if there is any identity element.

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