Lemma 15.84.12. Let $R$ be a ring. Let $K \in D(R)$ be given by a two term complex of the form $R^{\oplus n} \to R^{\oplus n}$. Denote $A \in \text{Mat}(n \times n, R)$ the matrix of the differential. Then $\det (a) : K \to K$ is zero in $D(R)$.

**Proof.**
Omitted. Good exercise.
$\square$

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