Mathematics - Quadratic Equation Question with Solution | TestHub

$$P{P}^T=\left[\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right]\left[\begin{array}{ccc}a& c& b\\ b& a& c\\ c& b& a\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$

$$\Rightarrow \left[\begin{array}{ccc}{a}^2+b^2+c^2& ab+bc+ca& ab+bc+ca\\ ab+bc+ca& a^2+b^2+c^2& ab+bc+ca\\ ab+bc+ca& ab+bc+ca& a^2+b^2+c^2\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$