Given, [P] = a_ij is a order 3 matrix.
Let $\mathrm{Q}=\left[\begin{array}{ccc}{2}^2{\mathrm{a}}_{11}& 2^3{\mathrm{a}}_{12}& 2^4{\mathrm{a}}_{13}\\ 2^3{\mathrm{a}}_{21}& 2^4{\mathrm{a}}_{22}& 2^5{\mathrm{a}}_{23}\\ 2^4{\mathrm{a}}_{31}& 2^5{\mathrm{a}}_{32}& 2^6{\mathrm{a}}_{33}\end{array}\right]$
$\mathrm{\mid }\mathrm{Q}\mathrm{\mid }=\mid \begin{array}{ccc}{2}^2{\mathrm{a}}_{11}& 2^3{\mathrm{a}}_{12}& 2^4{\mathrm{a}}_{13}\\ 2^3{\mathrm{a}}_{21}& 2^4{\mathrm{a}}_{22}& 2^5{\mathrm{a}}_{23}\\ 2^4{\mathrm{a}}_{31}& 2^5{\mathrm{a}}_{32}& 2^6{\mathrm{a}}_{33}\end{array}\mid$
$\Rightarrow \mathrm{Q}=2^2{2}^3{2}^4\left[\begin{array}{ccc}{\mathrm{a}}_{11}& {\mathrm{a}}_{12}& {\mathrm{a}}_{13}\\ 2{\mathrm{a}}_{21}& 2{\mathrm{a}}_{22}& 2{\mathrm{a}}_{23}\\ 2^2{\mathrm{a}}_{31}& 2^2{\mathrm{a}}_{32}& 2^2{\mathrm{a}}_{33}\end{array}\right]$
$\Rightarrow \mathrm{\mid }\mathrm{Q}\mathrm{\mid }=2^9\times 2\times 2^2\mid \begin{array}{ccc}{\mathrm{a}}_{11}& {\mathrm{a}}_{12}& {\mathrm{a}}_{13}\\ {\mathrm{a}}_{21}& {\mathrm{a}}_{22}& {\mathrm{a}}_{23}\\ {\mathrm{a}}_{31}& {\mathrm{a}}_{32}& {\mathrm{a}}_{33}\end{array}\mid$
⇒  |Q| = 2¹² |P|
⇒ |Q| = 2¹³