Which of the following sets with an internal binary operation does not have an inverse for every element? (a) Z2\{0} with the usual multiplication of residue classes. (b) Z\{0} with the usual multiplication of integers. (c) {[1 a;0 1]∈R^2×2 ∣ a∈R} with the usual multiplication of matrices. (d) C\{0} with the usual multiplication of complex numbers. (e) S^1={z∈C ∣ ∣z∣=1} with the usual multiplication of complex numbers.
Which of the following sets with an internal binary operation does not have an inverse for every element? (a) Z2\{0} with the usual multiplication of residue classes. (b) Z\{0} with the usual multiplication of integers. (c) {[1 a;0 1]∈R^2×2 ∣ a∈R} with the usual multiplication of matrices. (d) C\{0} with the usual multiplication of complex numbers. (e) S^1={z∈C ∣ ∣z∣=1} with the usual multiplication of complex numbers.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Question
Which of the following sets with an internal binary operation does not have an inverse for every element?
(a) Z2\{0} with the usual multiplication of residue classes.
(b) Z\{0} with the usual multiplication of integers.
(c) {[1 a;0 1]∈R^2×2 ∣ a∈R} with the usual multiplication of matrices.
(d) C\{0} with the usual multiplication of
(e) S^1={z∈C ∣ ∣z∣=1} with the usual multiplication of complex numbers.
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