Answer:
Option D
Explanation:
Concept Involved it is a simple question on scalar multipication i.e,
$\begin{bmatrix}ka_{1} & ka_{2}&ka_{3} \\b_{1} & b_{2}&b_{3}\\c_{1}&c_{2}&c_{3} \end{bmatrix}=k \begin{bmatrix}a_{1} & a_{2}&a_{3} \\b_{1} & b_{2}&b_{3}\\c_{1}&c_{2}&c_{3} \end{bmatrix}$
Description of Situation Construction of Matrix
i.e, if A=$ [a_{ij}]_{3\times 3}= \begin{bmatrix}a_{11} & a_{12}&a_{13} \\a_{21} & a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{bmatrix}$
sol. here , P=$[a_{ij}]_{3\times 3}= \begin{bmatrix}a_{11} & a_{12}&a_{13} \\a_{21} & a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{bmatrix}$
$Q=[b_{ij}]_{3x3}= \begin{bmatrix}b_{11} & b_{12}&b_{13} \\b_{21} & b_{22}&b_{23}\\b_{31}&b_{32}&b_{33} \end{bmatrix}$
where $b_{ij}=2^{i+j}a_{ij}$
$\therefore$ $|Q|= \begin{bmatrix}4a_{11} & 8a_{12}&16a_{13} \\8a_{21} &16 a_{22}&32a_{23}\\16a_{31}&32a_{32}&64a_{33} \end{bmatrix}$
=$4 \times 8 \times 16 \begin{bmatrix}a_{11} & a_{12}&a_{13} \\2a_{21} & 2a_{22}&2a_{23}\\4a_{31}&4a_{32}&4a_{33} \end{bmatrix}$
=$2^{9} \times 2 \times 4 \begin{bmatrix}a_{11} & a_{12}&a_{13} \\a_{21} & a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{bmatrix}$
=$2^{12}.|P|=2^{12}.2=2^{13}$
