I have a $2\times2$ block matrix $M$ defined as follows:
$$\begin{pmatrix}X+|X| & X-|X| \\ Y-|Y| & Y+|Y|\end{pmatrix}$$
where $X$ and $Y$ are $n\times n$ matrices and $|X|$ denotes the modulus of the entire matrix $X$ that essentially comprises modulus of individual elements of $X$.
How may I find the determinant of the matrix $M$ in terms of $X$ and $Y$? Looking for a simplified solution?