Let $A=\left[\begin{matrix}\frac{1}{\sqrt{2}} & -2 \ 0 & 1\end{matrix}\right]&P=\left[\begin{matrix}\cos \theta & -\sin \theta \ \sin \theta & \cos \theta \end{matrix}\right],\theta 0$. If $B=PA{P}^{T},C={P}^{T}{B}^{10}P&$ the sum of the diagonal element of ' $c$ ' is $\frac{m}{n}$ where $gcd(m,n)=1$, then (m+n) is

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Let $A=\left[\begin{matrix}\frac{1}{\sqrt{2}} & -2 \ 0 & 1\end{matrix}\right]&P=\left[\begin{matrix}\cos \theta & -\sin \theta \ \sin \theta & \cos \theta \end{matrix}\right],\theta >0$. If $B=PA{P}^{T},C={P}^{T}{B}^{10}P&$ the sum of the diagonal element of ' $c$ ' is $\frac{m}{n}$ where $gcd(m,n)=1$, then (m+n) is

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Let \(A=\left[\begin{matrix}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{matrix}\right]&P=\left[\begin{matrix}\cos \theta & -\si…

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