Max determinant

Question

Working on a 5x5 matrix the max determinant I figured out so far is 4.The entries I'm using is 0 and 1 . Is that the only determinant or is there bigger determinant than 4?

Answer 1

This is the Hadamard maximum determinant problem when $n=5$. The maximum possible determinant should be $5$, which is realised by, for instance, the following matrix: $$ \pmatrix{ 1&1&0&1&0\\ 0&0&0&1&1\\ 0&0&1&1&0\\ 1&0&1&0&1\\ 0&1&1&0&1}. $$