Maximum determinant of $3 \times 3$ matrix Good one guys! 
I'm studying to the maths olympiads in my college and I ran to the following problem:
What is the possible matrix $3 \times 3$, that you can write using digits from $0 $ to $9$, (you can repeat them), that gives you the maximum determinant?
I got by brute force the matrix:
\begin{pmatrix}
0 && 9 && 9\\
9 && 0 && 9 \\
9 && 9 && 0\\
\end{pmatrix}
Are there any other ways to do it besides brute force?
I looked about Hadamard maximum determinant theorem but I did not get how to apply it.
Thanks in advance =)

More generally, consider the $n \times n$ case.
Since the determinant is a linear function of the entries in any given row or column, it's clear that there is an optimal solution with all entries $0$ or $9$.  Dividing by $9$, you have an $n \times n$ $0-1$ matrix with maximum determinant, and that corresponds to a normalized solution of the  $(n+1) \times (n+1)$  Hadamard maximal determinant problem.
