• # question_answer Let $A=[{{a}_{ij}}]$ be a matrix of order $3\times 3$ and $B=[{{b}_{ij}}]$ be another matrix of order $3\times 3$ such that ${{b}_{ij}}$ is the sum of the elements of ${{i}^{th}}$ row of A except${{a}_{ij}}$. If det. $(A)=3,$ then the value of det. $(B)$ is equal to A) $2$                       B)        $4$                      C) $6$         D)        $8$

[c] $A=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} & {{a}_{13}} \\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}} \\ {{a}_{31}} & {{a}_{32}} & {{a}_{33}} \\ \end{matrix} \right]$  and  $|A|=3$ According to the question, $B=\left[ \begin{matrix} {{a}_{12}}+{{a}_{13}} & {{a}_{11}}+{{a}_{13}} & {{a}_{11}}+{{a}_{12}} \\ {{a}_{22}}+{{a}_{23}} & {{a}_{21}}+{{a}_{23}} & {{a}_{21}}+{{a}_{22}} \\ {{a}_{32}}+{{a}_{33}} & {{a}_{31}}+{{a}_{33}} & {{a}_{31}}+{{a}_{32}} \\ \end{matrix} \right]$ $\Rightarrow \,\,|B|\,\,=\,\,\left| \begin{matrix} {{a}_{11}} & {{a}_{12}} & {{a}_{13}} \\ {{a}_{21}} & {{a}_{22}} & {{a}_{23}} \\ {{a}_{31}} & {{a}_{32}} & {{a}_{33}} \\ \end{matrix} \right|\,\,\left| \begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{matrix} \right|=3\times 2=6$