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Let R is ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), (c, d)ER^2 then (a, b)* (c, d) =(a+c, b+d) and (a, b)0 (c, d) =(ac-bd, ad+bd) , Prove that(R^2, *, O) is * commutative ring with identity

Let R is ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), (c, d)ER^2 then (a, b)* (c, d) =(a+c, b+d) and (a, b)0 (c, d) =(ac-bd, ad+bd) , Prove that(R^2, *, O) is * commutative ring with identity

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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Let Ris ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), A (c, d)ER^2 then (a, b)* (c, d) =(a+c, b+d) and (a, b)0 (c, d) =(ac-bd, ad+bd) , Prove that(R^2, *, 0) is commutative ring with identity
Transcribed Image Text:Let Ris ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), A (c, d)ER^2 then (a, b)* (c, d) =(a+c, b+d) and (a, b)0 (c, d) =(ac-bd, ad+bd) , Prove that(R^2, *, 0) is commutative ring with identity
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