Question

If $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and $A^2$=I then x=__

Answer 1

$A^2=A.A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$

$\to \left[\begin{array}{cc}{x}^2+1& x\\ x& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Comparing the elements of the matrices, we get x = 0