Determinant/Multiplication theorem/Fact

Multiplication theorem for determinant

Let ${}K$ denote a field, and ${}n\in \mathbb {N} _{+}$.

Then for matrices

${}A,B\in \operatorname {Mat} _{n}(K)$, the relation

${}\det {\left(A\circ B\right)}=\det A\cdot \det B\,$

holds.

Proof, Write another proof