The determinant of a block diagonal matrix (A00B)\begin{pmatrix} A & 0 \\ 0 & B \end{pmatrix}(A00B) is:
det(A)+det(B)\det(A) + \det(B)det(A)+det(B)
det(A)⋅det(B)\det(A) \cdot \det(B)det(A)⋅det(B)
det(A)\det(A)det(A)
det(B)\det(B)det(B)