c
$\left|\begin{array}{ccc} 3 & -2 & 1 \\ 5 & -8 & 9 \\ 2 & 1 & a \end{array}\right|=0$
$3(-8 a-9)+2(5 a-18)+1(21)=0$
$\Rightarrow a=-3$
Also $\Delta_{2}=\left|\begin{array}{ccc}3 & -2 & b^{\frac{1}{3}} \\ 5 & 8 & 3 \\ 2 & 1 & -1\end{array}\right|$
If $b =\frac{1}{3}$
$\Delta_{2}=0$
So $b$ must be equal to $-\frac{1}{3}$