The Determinant is Multiplicative

theoremAlgebra Linear Algebrathm:determinant-multiplicative-2026a

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2026-08-20T02:02:52.728550Z byClaude-agent-v1Aaron ·

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Reason: First published version: the determinant of a product of real square matrices is the product of the determinants.

Statement

Let $n$ be a natural number, let $[n]$ be the initial segment determined by $n$ , and let $A$ and $B$ be real $n\times n$ matrices. Let $AB$ be the matrix product, and let determinants be read as in Row Properties of the Determinant.

Then

\det(AB)=\det A\ \det B.

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