How can I proof: Figure-Eight Knot is 5-colorable?

Question

I am learning Knot Theory recently. So I am doing some hand calculation for to find p-color for a Knot. So my current understanding says that A given Knot can be p-colorable if and only if the Knot can be split into a matrix M and det(M) follows p/det(M)

Here is a Figure-8 Knot image

From there I made a matrix: $ \begin{bmatrix} -1 &-1 &2 &0 \\ 0 &-1 &-1 &2 \\ -1 & 2 & 0 & -1 \\ 2 & 0 & -1 & -1 \end{bmatrix} $

Now I am trying to calculate its determinant and I got $18$, But it shouldn't happen cause Figure-8 will be then 3 and 6 colorable, but 6 colorable is absurd, as $p$ should be prime number.

So I need help about how can I proof 5-colorability for Figure-8 Knot? Is my understanding is incorrect?

Update: I solved it and have been able to calculated determinant 5. My mistake was to forgot to remove 1 column and 1 row to calculate the det.