€ {A R2×2 | det A = 1}. {A R2×2 | det A 0}. {A E R2×2 | AA = I}

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 24E
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Which of the following subsets in the set R^2×2 is not a group under the usual matrix multiplication operation?

(a) {A € R2×2 | det A = 1}.
(b) {A R2×2 | det A 0}.
(c) {A € R2×2 | AA₁ = I}
(d) {A € R²×² | A² = I}
(e) { [
cos
- sin
sin
cos
€ R²x² | pЄR}.
Transcribed Image Text:(a) {A € R2×2 | det A = 1}. (b) {A R2×2 | det A 0}. (c) {A € R2×2 | AA₁ = I} (d) {A € R²×² | A² = I} (e) { [ cos - sin sin cos € R²x² | pЄR}.
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