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Let \(P_1=I=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right], P_2=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]\),\(\begin{aligned}& P_3=\left[\begin{array}{lll}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{array}\right], P_4=\left[\begin{array}{lll}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{array}\right], P_5=\left[\begin{array}{lll}0 & 0 & 1 \\1 & 0 & 0 \\0 & 1 & 0\end{array}\right], \\& P_6=\left[\begin{array}{lll}0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0\end{array}\right] \text { and } X=\sum_{k=1}^6 P _{ K }\left[\begin{array}{lll}2 & 1 & 3 \\1 & 0 & 2 \\3 & 2 & 1\end{array}\right] P _{ K }^{ T }\end{aligned}\)where \(P_K^T\) denotes the transpose of the matrix \(P_K\). Then which of the following options is/are correct? 📲PW App Link - https://bit.ly/YTAI_PWAP 🌐PW Website - https://www.pw.live