Determinant_of_Matrix_Product

Let $\mathbf A = \sqbrk a_n$ and $\mathbf B = \sqbrk b_n$ be a square matrices of order $n$. Let $\map \det {\mathbf A}$ be the determinant of $\mathbf A$. Let $\mathbf A \mathbf B$ be the (conventional) matrix product of $\mathbf A$ and $\mathbf B$. Then $\map \det {\mathbf A \mathbf B} = \map \det {\mathbf A} \map \det {\mathbf B}$ That is, the determinant of the product is equal to the product of the determinants.