> [!Definiton] Definition (Scalar multiplication) > Let $(R,+,\circ)$ be a [[Rings|ring]]. Let $A$ be a [[Matrix|matrix]] over $R$ of order $m\times n.$ Let $\lambda\in \mathbb{R}.$ Then $\lambda A$ is given by the matrix $C$ whose $(i,j)$ entry is given by $c_{ij}=\lambda \circ a_{ij}$for all $(i,j)\in[1,2,\dots,m]\times[1,2,\dots,n].$