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

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

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

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

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