Denote by ×7 the operation “multiplication modulo 7” where ? ×7 ? is the remainder when ? × ? is divided by 7. 1. Construct the operation table for ×7 on the set ℤ?. 2. What is the identity element of ℤ? under ×7? 3. Determine the inverse of each element of ℤ7 with respect to ×7.
Denote by ×7 the operation “multiplication modulo 7” where ? ×7 ? is the remainder when ? × ? is divided by 7. 1. Construct the operation table for ×7 on the set ℤ?. 2. What is the identity element of ℤ? under ×7? 3. Determine the inverse of each element of ℤ7 with respect to ×7.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 6E
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Denote by ×7 the operation “multiplication modulo 7”
where ? ×7 ? is the remainder when ? × ? is divided by 7.
1. Construct the operation table for ×7 on the set ℤ?.
2. What is the identity element of ℤ? under ×7?
3. Determine the inverse of each element of ℤ7 with respect to ×7.
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