If $A$ and $B$ are square matrices of order three, then the determinant $\det (AB)$ is equal to:

Step 1 (Determinant Product Rule): A fundamental theorem of matrix algebra states that the determinant of the product of two square matrices of the same order is equal to the product of their individual determinants:

Step 2 (Order independence): This property holds true for square matrices of any order, including order three.

Step 3 (Conclusion): The determinant $\det (AB)$ is exactly $\det (A)\cdot \det (B)$, corresponding to option index 0.