Consider the matrix transformation $\mathbf{Y=AX}$, where $\mathbf Y$, $\mathbf A$, and $\mathbf X$ are all matrices. If $\mathbf A$ is a determinant and square matrix we know the differential entropy satisfying $$h(\mathbf Y)=h(\mathbf X)+\log\det(\mathbf A).$$
What if determinant matrix $\mathbf A$ is not square?