Question

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

• A. 9
• B. 7
• C. 5
• D. 3
• E. 13

Answer 1

Answer: (E)

There are only three determinants of second order with negative value,
$\begin{vmatrix}0&1\\ 1&0\end{vmatrix}\begin{vmatrix}0&1\\ 1&1\end{vmatrix}\begin{vmatrix}1&1\\ 1&0\end{vmatrix}$
Number of possible determinants with elements $0$ and $1$ are $2^{4}=16$
Hence, number of determinants with non-negative value is $13$ .