Mathematics - Determinant Question with Solution | TestHub

$|Q|=\left|\begin{array}{lll}{2}^2{a}_{11}& 2^3{a}_{12}& 2^4{a}_{13}\\ 2^3{a}_{21}& 2^4{a}_{22}& 2^5{a}_{23}\\ 2^4{a}_{31}& 2^5{a}_{32}& 2^6{a}_{33}\end{array}\right|$ $=2^2\cdot 2^3\cdot 2^4\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ 2a_{21}& 2a_{22}& 2a_{23}\\ 2^2{a}_{31}& 2^2{a}_{32}& 2^2{a}_{33}\end{array}\right|$ $=2^9\cdot 2\cdot 2^2\left|\begin{array}{lll}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|$ $=2^{12}\times |P|=2^{12}\times 2=2^{13}$