Let $R=M_{n}(Z_{2})$, can we write every matrices of $R$ as sum of two matrices of $GL_{n}(Z_{2})$?
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closed as not a real question by Victor Protsak, Loop Space, Akhil Mathew, Yemon Choi, Qiaochu Yuan Aug 23 '10 at 21:20It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. 


It appears you are asking whether $R$ is a 2good ring. The answer is yes. You may find the paper "2good rings" by Peter Vamos to be useful in giving you some background information. 

