Problem

$$A = \begin{pmatrix} 1 & k & 2 \\ 5 & 3 & -2 \\ 6 & -1 & 4 \end{pmatrix}$$

where $k$ is a constant.

(a) Determine the value of $k$ for which A is singular.

Given that A is non-singular,

(b) determine $A^{-1}$, giving your answer in simplest form in terms of $k$.