Let $$P = \begin{bmatrix}3 & -1 & -2 \\2 & 0 & \alpha \\3 & -5 & 0 \end{bmatrix}$$ where $$\alpha \in R$$. Suppose $$Q = [q_{ij}]$$ is a matrix such that $$PQ = kI$$, where $$k \in R, k \neq 0$$ and $$I$$ is the identity matrix of order 3. If $$q_{23} = -\frac{k}{8}$$ and $$det(Q) = \frac{k^2}{2}$$, then

A

$$\alpha = 0, k = 8$$

B

$$4 \alpha - k + 8 = 0$$

C

$$det(P adj(Q)) = 2^9$$

D

$$det(Q adj(P)) = 2^{13}$$