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a a Let G={ a ER, the real numbers, and a#0}. Let O be the usual matrix multiplication of matrices. a a Show that (G,O) is an Abelian group by verif ying explicitly all the axioms of an Abelian group. You may use that for all a and b in R, if a #0 and b#0 then ab# 0. Also, if a 0 then –is a real number which is not 0.

a a Let G={ a ER, the real numbers, and a#0}. Let O be the usual matrix multiplication of matrices. a a Show that (G,O) is an Abelian group by verif ying explicitly all the axioms of an Abelian group. You may use that for all a and b in R, if a #0 and b#0 then ab# 0. Also, if a 0 then –is a real number which is not 0.

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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Abstract Algebra 1
a a Let G={ a ER, the real numbers , and a ±0}. Let © be the usual matrix multiplication of matrices. a a Show that (G,0) is an Abelian group by verif ying explicitly all the axioms of an Abelian group. You may use that for all a and b in R, if a #0 and b#0 then ab# 0. 1 Also, if a 0 then –is a real number which is not 0. a
Transcribed Image Text:a a Let G={ a ER, the real numbers , and a ±0}. Let © be the usual matrix multiplication of matrices. a a Show that (G,0) is an Abelian group by verif ying explicitly all the axioms of an Abelian group. You may use that for all a and b in R, if a #0 and b#0 then ab# 0. 1 Also, if a 0 then –is a real number which is not 0. a
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