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Given two matrices of equal order $m\times n$, $A=(a_{ij})_{ij}$ and $B=(b_{ij})_{ij}$, we define its sum as another matrix of order $m\times n$ given by

$$A+B = (a_{ij}+b_{ij})_{ij} = \left(\begin{array}{cccc} a_{11}+b_{11} & a_{12}+b_{12} & \cdots & a_{1n}+b_{1n}\\ a_{21}+b_{21} & a_{22}+b_{22} & \cdots & a_{2n}+b_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ a_{m1}+b_{m1} & a_{m2}+b_{m2} & \cdots & a_{mn}+b_{mn}\\ \end{array}\right)$$

whose coefficients are the corresponding sum of the elements of $A$ and $B$. This is why the sum is only defined for matrices of the same order