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The Existence of Multiplicative Inverse

by R. Alfaro and S. Althoen

This article originally appeared in:
College Mathematics Journal
May, 2006

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Fields | Algebra | Algebraic Proof | Linear Algebra | Systems of Linear Equations
Applicable Course(s): 3.8 Linear/Matrix Algebra | 4.2 Mod Algebra I & II

This capsule discusses a way to show each non-zero element of certain rings have a multiplicative inverse. The approach is to set up a system of linear equations and the solution is the multiplicative inverse. Therefore the non-zero determinant guarantees the existence of the multiplicative inverse.

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Capsule Course Topic(s):
One-Variable Calculus | Infinite Limits: Sequences and Series
Linear Algebra | Determinants
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