JEE Math Practice Question
Let $\beta$ be a real number. Consider the matrix \[ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{array}\right) \] If $A^{7}-(\beta-1) A^{6}-\beta A^{5}$ is a singular matrix, then what is the value of $9 \beta$?
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