GATE 2022 CE (CE2) – Question 30
$\varepsilon=\begin{bmatrix}1&1\\1&-1\end{bmatrix}$. Given $P=\operatorname{tr}(\varepsilon^8)$ and $Q=\operatorname{tr}(\varepsilon^{11})$, find P+Q (integer).
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Correct answer: 32
Explanation
Multiplication gives $\varepsilon^2=2I$. Hence $\varepsilon^8=16I$ and P=32. Also $\varepsilon^{11}=32\varepsilon$, whose trace is zero.
Therefore **P+Q=32**.