Addition on [[Matrix|Matrices]] is [[Linear]], and follows the same scaling rule as [[Vector|Vectors]] $\huge \begin{align} \forall A,B\in M_{n\times m} &\, \ba{ {A+B}\in M_{n\times m} } \\ \pa{A+B}_{i,j} &= a_{i,j} + b_{i,j} \end{align} $ $\huge \begin{align} \let A \in M_{n,n} &= \mat{\vec A_{1}, \dots,\vec A_{n}}\\ \let k &\in \R \\ kA &= \mat{k\vec A_{1}, \dots ,k\vec A_{n}}\\ \end{align} $