c
(c) Applying ${C_1} \to {C_1} + {C_2} + {C_3}$, we obtain
$ - x\,\left| {\,\begin{array}{*{20}{c}}1&{ - 6}&3\\1&{3 - x}&3\\1&3&{ - 6 - x}\end{array}\,} \right|$ = 0
$ \Rightarrow $ $ - x\,\left| {\,\begin{array}{*{20}{c}}1&{ - 6}&3\\0&{9 - x}&0\\0&9&{ - 9 - x}\end{array}\,} \right| = 0$
$ \Rightarrow $ $ - x(9 - x)\,( - 9 - x) = 0 \Rightarrow x = 0,\,9,\, - 9$.
Trick : Check by assuming the values of $x$ from the given options.