In the ring of 2 x 2 matrices over the real numbers M2(R) what is true of the set of all matrices having this form O b cd ? A) It is both a subring and an ideal B It is a subring but not an ideal C) It is an ideal but not a subring D) It is neither an ideal nor a subring

Q: Show that for any two finite-dimensional L-representations V and W of L: (a) Hom (V, k) ~V* as…

A: To show that for any tow finite-dimensional L-representation V and W of L HomkV, W≃V*⊗W as L-module

Q: Prove by induction the Determinants of all Cartan matrices corresponding to simple finite…

A: In induction Method first of all we selected for some cases then we write its true for all other…

Q: (1) Find all left, right and two-sided ideals of the ring of n x n complex matrices.

A: All left, right, and two-sided ideals of the ring of n×n matrices are determined.

Q: If A and B are arbitrary real m X n matrices, then the mapping (A, B) = trace(A" B) defines an inner…

A:

Q: 1. Consider the set of upper triangular 2 x 2 matrices, with real entries: b B = {(" "); GAVER} a,…

A: We have to prove that U is an ideal in B.

Q: Does there exists a (non-commutative) ring of 2x2 matrices over the rationals contains a subring…

A: And,

Q: Let R be a field of real numbers and M₂(R) be a ring of 2 x 2 matrices over R under usual…

A:

Q: 4) Let R be a ring and F-M₂(R) be ring of 2 x 2 matrices over R under standard addition and…

A: # Answer 4) Given:- R  is a ring.- F=M2​(R) , the ring of 2×2  matrices over R  under standard…

Q: Let M be the set of all 2 x 2 matrices with real entries, under ordinary matrix addition and matrix…

A: A ring is called a field if it has unit element, commutative under multiplication and inverse of…

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

A: In the given proof, we showed that if I is an ideal in a commutative ring R, then the set M2​(I) of…