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.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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