Mathematics - Matrices Question with Solution | TestHub

$$\begin{array}{rl}& P(EP)=P\left[\begin{array}{ccc}1& 3& 2\\ 2& 4& 3\\ 8& 18& 13\end{array}\right]=\left[\begin{array}{ccc}1& 3& 2\\ 8& 18& 13\\ 2& 4& 3\end{array}\right]=F\\ & |E|=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 8& 13& 18\end{array}\right](R_3\to R_3-3R_2-2R_1)=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 0& 0& 0\end{array}\right]\Rightarrow |F|=0\\ & |EQ+PF{Q}^{-1}|=|EQ+PPEP{Q}^{-1}|=|EQ+EP{Q}^{-1}|=|E||Q+P{Q}^{-1}|=0\\ & |EQ|=|E||Q|=0,|PF{Q}^{-1}|=|P||F||Q^{-1}|=0\end{array}$$