$AB=AD\text{ and }AD=b\text{ and }b=d$

$\left\{\begin{matrix}d=AD\text{, }&B=D\text{ and }b=AD\\d=0\text{, }&b=0\text{ and }A=0\end{matrix}\right.$

$\left\{\begin{matrix}b=AD\text{, }&B=D\text{ and }d=AD\\b=0\text{, }&A=0\text{ and }d=0\end{matrix}\right.$