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I'm trying to prove this:

Let $R$ be a ring, and $A \in M_n(R)$. Write $L_A$ for the linear map $L_A : R^n \to R^n$ determined by left multiplication by $A$. Shows that if $L_A$ is injective, then det($A$) is not a zero divisor.

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marked as duplicate by Pierre-Guy Plamondon, Namaste abstract-algebra Dec 28 '18 at 18:57

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