Let `A=[("tan"pi/3,"sec" (2pi)/3),(cot (2013 pi/3),cos (2012 pi))]` and P be a `2 xx 2` matrix such that `P P^(T)=I`, where `I` is an identity matrix of order 2. If `Q=PAP^(T)` and `R=[r_("ij")]_(2xx2)=P^(T) Q^(8) P`, then find `r_(11)`.

Explanation

To solve the problem, we will follow the steps outlined in the video transcript and derive the required value of \( r_{11} \) step by step.

### Step 1: Define the matrix \( A \)
We are given:
\[ A = \begin{pmatrix} \tan\left(\frac{\pi}{3}\right) & \sec\left(\frac{2\pi}{3}\right) \\ \cot\left(\frac{2013\pi}{3}\right) & \cos\left(2012\pi\right) \end{pmatrix} \]

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