Matrices - Addition and Subtraction of Matrices

Given that \(\mathbf{A} = \begin{pmatrix} 3 & -1 \\ -2 & 1 \end{pmatrix}\), \(\mathbf{B} = \begin{pmatrix} 2 & k \\ 4 & 1 \end{pmatrix}\) and \(\mathbf{C} = \begin{pmatrix} 3 & 4 \\ 0 & 1 \end{pmatrix}\),

1. find \(\mathbf{A}^2 + 2\mathbf{B}\) in terms of \(k\).
2. If \(\mathbf{A}^2 + 2\mathbf{B} = 5\mathbf{C}\), find the value of \(k\).