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Assignment Topic - Abstract Algebra

Q1: Let R be the ring of all 2 X 2 matrices over Zp, p is a prime. Let G be the set of elements x in the ring R such that det(x) ≠ 0. Find the order of G.

Q2: If R is a commutative ring with 1 and R has no ideals other than (0) and itself, prove that R is a field.

Q3: Let G be a non-abelian group of order 6. Prove that G ≈ S3.

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### Assignment topic - abstract algebraq1 let r be the ring of

Assignment Topic - Abstract Algebra Q1: Let R be the ring of all 2 X 2 matrices over Z p , p is a prime. Let G be the set of elements x in the ring R such that det(x) ≠ 0. Find the order of G. Q2: If R is a commutative r ...

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