Addition of matrices

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Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:

$\mathbf{A}+\mathbf{B}= \left[\begin{array}{cccc} a_{11} & a_{12} & \dots &a_{1n} \\ a_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1} & \dots & & a_{mn} \end{array}\right]+ \left[\begin{array}{cccc} b_{11} & b_{12} & \dots &b_{1n} \\ b_{21} &\ddots & &\vdots\\ \vdots & & & \\ b_{m1} & \dots & &b_{mn} \end{array}\right]= \left[\begin{array}{cccc} a_{11}+b_{11} & a_{12}+b_{12} & \dots &a_{1n}+b_{1n} \\ a_{21}+b_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} \end{array}\right]$

Example: Addition of two 3-by-3 matrices $\mathbf{A}_e+\mathbf{B}_e= \left[\begin{array}{ccc} 1 & 3 & -2\\ 0 & -1 & 3\\ 2 & 4 & 2 \end{array}\right]+ \left[\begin{array}{ccc} -3 & 2 & -1\\ 2 & 4 & -3\\ 0 & -2 & 1 \end{array}\right]= \left[\begin{array}{ccc} 1-3 & 3+2 & -2-1\\ 0+2 & -1+4 & 3-3\\ 2+0 & 4-2 & 2-1 \end{array}\right]= \left[\begin{array}{ccc} -2 & 5 & -3\\ 2 & 3 & 0\\ 2 & 2 & 1 \end{array}\right]$