19. Let $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 4 \\ 2 & 6 \end{bmatrix}$. If it is known that $AB = \begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$, what is the unique solution to the system $ax + by = 10$ and $cx + dy = -2$?
A: $(17, -6)$
B: $(34, -12)$
C: $(12, 8)$
D: $(24, 16)$
E: $(6, 4)$