Question

If A = $\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and $A^2$ is identity matrix, then $x=$

• A. $1$
• B. $-1$
• C. $\pm 1$
• D. $0$

Answer 1

The correct option is D $0$

Since, $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right],A^2=I$
$A^2=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}{x}^2+1& x\\ x& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
$\Rightarrow$ So $x=0$
Option D is the correct answer.