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