Answer
Use theorem 6:
$$\det(AB)=\det(A)\det(B)=\det(B)\det(A)=\det(BA)$$
Work Step by Step
We make use of theorem 6, which holds since both $A$ and $B$ are square matrices:
$$\det(AB)=\det(A)\det(B)$$
It follows from commutativity of the real, and complex, numbers that
$$\det(A)\det(B)=\det(B)\det(A)$$
We now use theorem 6 again, and put the whole thing together:
$$\det(AB)=\det(A)\det(B)=\det(B)\det(A)=\det(BA)$$
Since we have said nothing of wether $AB=BA$, this holds for any two square matrices.
