Bounding the determinant of principal sub-matrices of the Kroneker product

Question

I have a matrix $A$ that is 2 dimensional and has negative determinant. I have a matrix $B$ that is 2 dimensional and has a positive determinant. Both have strictly positive elements. I want to show that $A\circ B$ has a non-positive determinant, where $\circ$ is the Hadamard product. One possible avenue is that $A\circ B$ is a principle sub-matrix of $A\otimes B$, which may allow one to bound the eigenvalues of the sub-matrix $A\circ B$.