Does every square matrix on a division ring which has a left inverse have also a right inverse?
2026-02-23 02:37:14.1771814234
A question about inverse square matrix on division ring.
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Yes, for the same reason as over a field: if you interpret matrices as endomorphisms of vector spaces, then left/right invertibility corresponds to surjectivity or injectivity, and over division rings an injective/surjective linear map between finite dimensional spaces of the same dimension is an isomorphism (because there is a well-behaved theory of dimension).