Using a geometric argument, explain why the matrix below has maximal absolute determinant among all matrices with entires in {-1,1}.

$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & 1 & -1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1 \end{bmatrix}$

I believe this has something to do with the fact that each sub matrix is either a rotation or a reflection and there is a symmetric number of both. Does this thinking seem in line with others?