Question

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

• A. $0$
• B. $10$
• C. $13$
• D. $20$

Answer 1

The correct option is C $13$

There are only three determinants of second order with negative values, viz.

$\left|\begin{array}{cc}0& 1\\ 1& 0\end{array}\right|,\left|\begin{array}{cc}0& 1\\ 1& 1\end{array}\right|,\left|\begin{array}{cc}1& 1\\ 1& 0\end{array}\right|$

The number of possible determinants with elements $0$ and $1$ is $2^4=16.$ Therefore number of determinants with non-negative values is $13.$