\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For any square matrix \(\mathbf{A}\), expand and simplify the expression \((\mathbf{A}+\mathbf{I})^2\), where \(\mathbf{I}\) is the identity matrix of the same order as \(\mathbf{A}\).
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