Find the maximal determinant of a $4n \times 4n$ matrix with $2n$ entries equal to $1$ and $2n$ entries equal to $-1$.
My attempt:
For $n=1$, we take the following matrix:
\begin{pmatrix} 1 & 0 & -1 & -1 \\ 0 & 1 & 0 & 0\\ 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 2 \end{pmatrix}
But, instead of $2$ I would put any other value, so does this determinant diverge?