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:

Failed to parse (syntax error): \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{pmatrix}\right]+ \begin{pmatrix} b_{11} & b_{12} & \dots &b_{1n} \\ b_{21} &\ddots & &\vdots\\ \vdots & & & \\ b_{m1} & \dots & &b_{mn} \end{pmatrix} , \quad \mathbf{A}^T = \begin{pmatrix} a_{11} & a_{21} & \dots &a_{m1} \\ a_{12} &\ddots & &\vdots\\ \vdots & & & \\ a_{1n} & \dots & &a_{mn} \end{pmatrix}