Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{PQ}=\mathrm{QP}\Rightarrow \left[\begin{array}{ccc}2{\mathrm{a}}_1& 2{\mathrm{b}}_1& 2{\mathrm{c}}_1\\ 2{\mathrm{a}}_2& 2{\mathrm{b}}_2& 2{\mathrm{c}}_2\\ 3{\mathrm{a}}_3& 3{\mathrm{b}}_3& 3{\mathrm{c}}_3\end{array}\right]=\left[\begin{array}{ccc}2{\mathrm{a}}_1& 2{\mathrm{b}}_1& 3{\mathrm{c}}_1\\ 2{\mathrm{a}}_2& 2{\mathrm{b}}_2& 3{\mathrm{c}}_2\\ 2{\mathrm{a}}_3& 2{\mathrm{b}}_3& 3{\mathrm{c}}_3\end{array}\right]\\ & {\mathrm{c}}_1=0,{\mathrm{c}}_2=0,{\mathrm{a}}_3=0,{\mathrm{b}}_3=0\\ & \mathrm{Q}=\left[\begin{array}{ccc}{\mathrm{a}}_1& {\mathrm{b}}_1& 0\\ {\mathrm{a}}_2& {\mathrm{b}}_2& 0\\ 0& 0& {\mathrm{c}}_3\end{array}\right]\\ & {\mathrm{a}}_1{\mathrm{a}}_2+{\mathrm{b}}_1{\mathrm{b}}_2=0\\ & {\mathrm{a}}_1^2+{\mathrm{b}}_1^2=1,{\mathrm{a}}_2^2+{\mathrm{b}}_2^2=1,{\mathrm{c}}_3^2=1\end{array}$ $\begin{array}{lllll}{a}_1& b_1& a_2& b_2& c_3\\ 1& 0& 0& 1,-1& +1,-1\\ -1& 0& 0& 1,-1& 1,-1\\ 0& 1& 1,-1& 0& 1,-1\\ 0& -1& 1,-1& 0& 1,-1\end{array}$ Total 16 matrices