If $A$ and $B$ are matrices of the [[same size]], then $A+B$ is defined to be the matrix with the same size as $A$ and $B$ so that the $(i,j)$ entry of $A+B$ is $a_{ij}+b_{ij}$, for every $i,j$.

If $A$ and $B$ are matrices of different sizes, then $A+B$ is undefined.