What is the determinant of a block diagonal matrix $A = \begin{pmatrix} A_1 & 0 \\ 0 & A_2 \end{pmatrix}$ where $A_1 = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $A_2 = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}$?