1 The matrix \(\mathbf { A }\) is given by
$$\mathbf { A } = \left( \begin{array} { c c c }
k & 1 & 0
6 & 5 & 2
- 1 & 3 & - k
\end{array} \right)$$
where \(k\) is a real constant.
- Show that \(\mathbf { A }\) is non-singular.
- Given that \(\mathbf { A } ^ { - 1 } = \left( \begin{array} { c c c } 3 & 0 & - 1
1 & 0 & 0
- \frac { 23 } { 2 } & \frac { 1 } { 2 } & 3 \end{array} \right)\), find the value of \(k\).