In determinants, we have the property that $det(AB)=det(A)det(B)$, I believe this can also be extended to the product of three matrices i.e. $det(ABC)=det(A)det(B)det(C)$.
Given $X$ is a vector of order $nx1$ and $X'AX=0$ where matrix A has appropriate order.
So $det(X'AX)=0$, this implies that $det(X')det(A)det(X)=0$.
But X is not even a matrix, let alone be a square matrix, a necessary condition to define determinants.
Where did my reasoning go wrong?