A determinant of second order is made with the elements 0 and 1. The number of determinants with non-negative values is

There are only three determinants of second order with negative value.

$\left|\begin{array}{c}01\\ 10\end{array}\right|,\left|\begin{array}{c}01\\ 11\end{array}\right|,\left|\begin{array}{c}11\\ 10\end{array}\right|$  Number of possible determinants with elements 0 and 1 are $2^4=16.$  Therefore number of determinants with non-negative values is 13.