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2. Let H be the set of 2 x 2 matrices of the form a H = {( ₂² ) | ab € C} -b a, where a denotes the complex conjugate of a complex number a. Show that H, together with matrix addition and multiplication, forms a ring. (You may assume that M₂(C) is a ring.)

2. Let H be the set of 2 x 2 matrices of the form a H = {( ₂² ) | ab € C} -b a, where a denotes the complex conjugate of a complex number a. Show that H, together with matrix addition and multiplication, forms a ring. (You may assume that M₂(C) is a ring.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Let H be the set of 2 × 2 matrices of the form H a b = { (- / + d ) | a,b ≤ c } a where a denotes the complex conjugate of a complex number a. Show that H, together with matrix addition and multiplication, forms a ring. (You may assume that M₂(C) is a ring.)
Transcribed Image Text:2. Let H be the set of 2 × 2 matrices of the form H a b = { (- / + d ) | a,b ≤ c } a where a denotes the complex conjugate of a complex number a. Show that H, together with matrix addition and multiplication, forms a ring. (You may assume that M₂(C) is a ring.)
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