> [!NOTE] Lemma > Let $A$ be [[Real Matrices|real matrix]] with order $m\times n.$ Let $l,p\in \mathbb{N}^{+}.$ Let $0_{lm}$ denote the [[Real Zero Matrix|zero matrix of order]] $l\times m.$ Then we have the following [[Real Matrix Product|products]]: $0_{lm}A=0_{\ln}$ and $A 0_{np}=0_{mp}.$ **Proof**: We have $\begin{align} \text{the $(i, j)$th entry of $0_{lm} A$} &= \sum_{k=1}^{n} 0 a_{kj}=0\\\text{the $(i, j)$th entry of $A 0_{np}$}&=\sum_{k=1}^{m} a_{ik} 0=0\end{align}$