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.