c
$\Delta=\left|\begin{array}{ccc}{1} & {1} & {-a} \\ {2} & {a} & {1} \\ {a} & {1} & {-1}\end{array}\right|=1(-a-1)-1(-2-a)-a\left(2-a^{2}\right)$
$=a^{3}-2 a+1=(a-1)\left(a^{2}+a-1\right)$
$=(a-1)\left(a-\frac{-1-\sqrt{5}}{2}\right)\left(a-\frac{-1+\sqrt{5}}{2}\right)$
For $\Delta=0$
$a=1, \frac{-1 \pm \sqrt{5}}{2}$
for each value system has no solution.