Let r be the ring of all 2 x 2 matrices over zp p is a

Question

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 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.