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If \(P=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]\), then \(P^{50}\) is [JEE Main 2021, 25 Jul (S…

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If \(P=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]\), then \(P^{50}\) is

[JEE Main 2021, 25 Jul (Shift 2)]

a

\(\left[\begin{array}{cc}1 & 0 \\25 & 1\end{array}\right]\)

b

\(\left[\begin{array}{cc}1 & 50 \\0 & 1\end{array}\right]\)

c

\(\left[\begin{array}{cc}1 & 25 \\0 & 1\end{array}\right]\)

d

\(\left[\begin{array}{cc}1 & 0 \\50 & 1\end{array}\right]\)

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