🛠️ JEE➗ Maths

If \(A=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right], P=\left[\begin{array}{ll}1 & 1 \\ 0 & 1…

Q1

If \(A=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right], P=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\) and \(X=A P A^T\), then \(A^T X^{50} A\) is:

a

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

b

\(\left[\begin{array}{cc}2 & 1 \\ 0 & -1\end{array}\right]\)

c

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

d

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

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