# Sufficient and necessary condition for $\det(I+\Omega A)=\det(I-\Omega B)$?

What's the sufficient and necessary condition for $$\det(I+\Omega A)=\det(I-\Omega B)$$? Here, all the matrices are $$3\times3$$, $$\Omega$$ is skew-symmetric with its determinant equals to zero.

If the sufficient and necessary condition is difficult to find, what's the sufficient condition for this equation to be true? I know one of them is $$A^T=A=B$$ but it's too strict for my application.