Problem

The matrix $\mathbf{M}$ is defined by

$\mathbf{M} = \begin{pmatrix} k + 5 & -2 \\ -3 & k \end{pmatrix}$

(a) Determine the values of $k$ for which $\mathbf{M}$ is singular.

Given that $\mathbf{M}$ is non-singular,

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