Problem

$\mathbf{M} = \begin{pmatrix} 2k + 1 & k \\ k & k + 4 \end{pmatrix}$

where $k$ is a constant

(a) Show that $\mathbf{M}$ is non-singular for all real values of $k$.

(b) Determine $\mathbf{M}^{-1}$ in terms of $k$.