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Ok, so this is an extra credit question on a test, i haven't really tried it yet, but the test is thurs, so i figured i'd try to post this to see what anyone says, and then see what i work out, or whatever. I don't even know what "right ideals" means, but our prof said thats what the question was about... so i figured... ya...

Let R be a subspace of V = M(n,n) such that AB is in R whenever A is in R. Let W be the subspace of R_n spanned by all AX with A in R, X in R_n.

A) show that for any matrix A in M

i) Aej = Aj and ii) A= summation(AjeJ)

B) show that if AX is in W for every X in R_n then Aj is in W.

C) Write Aj as a linear combination of products A(ij)X(ij), A(ij) in R, X(ij) in R_n

D) use ii) to show that if A is as in B), then A is in R

E) show that R consists of all matrices A in M with AX in W for all X in R_n

OOOOK.... so thats the problem. The only hint he gave us was the "right ideals" thing. So i'll google that and see if i can work this all out in the morning. I pretty much have tons of trouble with this stuff though, so we'll see. Any help would be totally awesome! oh, and if you don't understand the question... join the club... i can try to explain his notation if its weird... but thats about it. thanks in advance...

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# Right ideals

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