• # question_answer Maximum value of the determinant of order third formed by the elements 0 & 1 only is A) 3 B) 2 C) 1 D) none of these

 Let $D=\left| \begin{matrix} {{a}_{11}} & {{a}_{12}} & {{a}_{13}} \\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}} \\ {{a}_{31}} & {{a}_{32}} & {{a}_{33}} \\ \end{matrix} \right|$ for maximum value we have to assign maximum value to the +ve term & minimum value to $ve$term which is possible if three elements will become zero of different row & different column. $\therefore$    i.e. ${{a}_{13}}={{a}_{21}}={{a}_{32}}=0$& ${{a}_{11}}={{a}_{32}}={{a}_{33}}={{a}_{12}}$ $\therefore$    ${{D}_{\max }}=2-0=2$