\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Given that a square matrix \(\mathbf{A}\) satisfies the relation \(\mathbf{A}^2 = \mathbf{A} + \mathbf{I}\), find the expressions for \(\mathbf{A}^3\) and \(\mathbf{A}^4\) in the linear form \(k\mathbf{A} + l\mathbf{I}\), where \(k\) and \(l\) are scalars and \(\mathbf{I}\) is the identity matrix.
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