If \( A=\begin{bmatrix}x & 1\\1 & 0\end{bmatrix} \) and \( A^2=I \), where \( I \) is an identity matrix of order 2, then value of \( x \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0
\( \displaystyle A^2=\begin{bmatrix}x & 1\\1 & 0\end{bmatrix}\begin{bmatrix}x & 1\\1 & 0\end{bmatrix} \)
\( \displaystyle =\begin{bmatrix}x^2+1 & x\\x & 1\end{bmatrix} \)
Equating corresponding entries with \( I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \):
\( x=0 \)
\( x^2+1=1 \), which also gives \( x=0 \)