Let $A, B, C$ be [[matrix|matrices]]. Assume: - $A, B$ can be [[matrix multiplication|multiplied]], - $A, C$ can be [[matrix multiplication|multiplied]], - $B, C$ can be [[matrix addition|added]]. Then $A$, and $B+C$ can be [[matrix multiplication|multiplied]] $ A(B+C)=A B+A C $ Which is verified by the [[distributive property]] of the [[dot product]] over [[vector addition]] $\mathbf{a}_{i®}\cdot(\mathbf{b}_{©k}+\mathbf{c}_{©k})=\mathbf{a}_{i®}\cdot\mathbf{b}_{©k}+\mathbf{a}_{i®}\cdot\mathbf{c}_{©k}$