# Injective ring endomorphism and determinant [duplicate]

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.