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For three square matrices of order 2, \(\mathbf{A}=\begin{pmatrix} x & y \\ z & w \end{pmatrix}\), \(\mathbf{B}=\begin{pmatrix} x' & y' \\ z' & w' \end{pmatrix}\), and \(\mathbf{C}=\begin{pmatrix} x'' & y'' \\ z'' & w'' \end{pmatrix}\), prove that \(\mathbf{A}+(\mathbf{B}+\mathbf{C}) = (\mathbf{A}+\mathbf{B})+\mathbf{C}\).
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