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Is it true that every left invertible square matrix Α over a division ring R is also right invertible? If that is the case and B is the left inverse of A and C is the right inverse of A , then B=C?

Edit: for the second question we have that, C=InC=(BA)C=B(AC)=BIn=B (where In is the identity matrix).

Any thoughts on the the 1st question?

Paranoi_D
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jun 17 '23 at 12:35
  • Yes. The exact same proof here works. It's possible because the familiar theory of bases from linear algebra also works for division rings. – rschwieb Jun 17 '23 at 13:46

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