4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard addition and multiplication of matrices then: a) F is a commutative ring but not field. b) F is a division ring and not field. c) If F an integral domain and F is not field. d) No one of above. 5) Let be a map from a space (X,7) in to a space (Y, 7) and 7" is a topology on Y such that TCT' then a) b) 1 c) d) If is T-continuous then is T-T continuous. Iff is T-7 continuous then is T-7" continuous. Iff is T-T open thenf is T-T open. If is T-T discontinuous then is T-T" discontinuous.

Q: 2. Which of the following is a basis for the space of polynomials of degree < 2 over R? (Check all…

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Q: . Let R be the ring of all complex numbers and R' the a b b a ring of all 2 x 2 matrices of the form…

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Q: Prove that (Z O Z)(a, 0)) × {(0, b))) is isomorphic to Z, O Z,.

A: To Prove: Z⊕Z/a, 0×0, b is isomorphic to Za⊕Zb.

Q: 7. If f(x) is irreducible over R, then f (x²) is irreducible over R. a) True b) False

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Q: A) Let A = {1,2, 3, 4} and R a relations on A whose matrices [1 1 1 1] 0 1 1 1 is MR = %3D 0 011 [o…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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Q: Show that the set of all matrices of order 2×2 of the  form \matrix{a|0|b|c}, where a,b,c are…

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Q: Let R₁ and R₂ be relation on a set A represented by the matrices [0 1 0] 1 1 0 го о 17 MR₁ = 0 1 0…

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Q: Prove that there exists a countable basis for the product space R2022

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Q: Let R be a commutative ring and M₂(R) the ring of 2-by-2 matrices with entries in R (with the usual…

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A: Since you have posted multiple questions, we will provide the solution only to the first question…