# Question about ideal of a ring

by DukeSteve
Tags: abstract algebra, ideals, rings
 P: 10 Hello Experts, Again a Q and what I did, please tell me what I am doing wrong: Given that there is a ring of matrices above Z (integers) Mn(Z) and 2 ideals I, J of this ring. I need to prove that they are commutative: IJ = JI What I did is that: For all i in I and for all M in Mn(Z) n is the the size of a matrix n x n M*i in I and i*M is also in I. same with J : j*M in J and M*j is in J For every k in J and for every h in I: kh = j*M*i*M = j*(M*i)*M = .... I don't know what to do from here.... please guide me.
 P: 1 Hey Duke! I suggest you to check again your hypothesys instead. Well, $$\mathbb{Z}$$ is a ring with unity, right? What's the form of it's ideals? What's the form of the ideals of $$M_{n}(\mathbb{Z})$$? The problem of your approach is that I can't really see a way to use your hypothesys.

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