Let $\beta$ be a real number. Consider the matrix
$$A = \left( \begin{array} { c c c }
\beta & 0 & 1 \\
2 & 1 & - 2 \\
3 & 1 & - 2
\end{array} \right)$$
If $A ^ { 7 } - ( \beta - 1 ) A ^ { 6 } - \beta A ^ { 5 }$ is a singular matrix, then the value of $9 \beta$ is $\_\_\_\_$ .