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.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.

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