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Unformatted text preview: (a) An element of Mat n .R/ is invertible if, and only if, its determi-nant is a unit in R . (b) If an element of Mat n .R/ has a left inverse or a right inverse, then it is invertible Proof. We have already seen that the determinant of an invertible matrix is a unit (Corollary 8.3.9 (e)). On the other hand, if det .A/ is a unit in R , then det .A/ 1 C t is the inverse of A . If A has a left inverse, then its determinant is a unit in R , so A is invertible by part (a). n...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08