Question:

Let $A$ be a square matrix of order $3$ such that $A + A^T = \begin{bmatrix} 10 & 4 & 6 \\ 4 & 6 & -1 \\ 6 & -1 & 8 \end{bmatrix}$ where $a_{ij}, a_{ji}, a_{kj}$ are positive roots of the equation $x^3 - 6x^2 + px - 8 = 0, \forall c \in \mathbb{R}$, then the absolute value of $|A|$ is equal to