Addition of Matrices

Two matrices can be added only when they have exactly the same order — you cannot add a $2 \times 3$ matrix to a $3 \times 2$ matrix, since there is no sensible way to pair up their elements. When $A = [a_{ij}]$ and $B = [b_{ij}]$ are both of order $m \times n$, their sum $S = A + B$ is the matrix of the same order obtained by adding corresponding elements: