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  4. The maximum and minimum value of (3 × 3) determinant whose elements belongs to 0,1 is

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Q. The maximum and minimum value of $(3 \times 3)$ determinant whose elements belongs to $\{0,1\}$ is

Determinants

Solution:

$\left|A\right|_{max} =\begin{bmatrix}0&1&1\\ 1&0&1\\ 1&1&0\end{bmatrix}=0-\left(-1\right)+1\left(1\right)2$
$\therefore \left|A\right|_{min}=-2$