> [!Definition] Definition (Matrix addition) > Let $(R,+,\circ)$ be a [[Rings|ring]]. Let $A,B$ be [[Matrix|matrices]] over $R$ of the same order. The sum of $A$ and $B,$ denoted $A+B,$ is the matrix $C\in R^{m\times n}$ whose $(i,j)$ entry is given by $c_{ij}=a_{ij}+b_{ij}$for all $(i,j)\in[1,2,\dots,m]\times[1,2,\dots,n].$