Statement-I : If $\mathrm{A}=\left[\begin{array}{cc}\mathrm{x}& 1\\ 1& 0\end{array}\right]$ is an Involutory matrix then x = 0 

Statement-II : If A = $\left[\begin{array}{cc}0& -\mathrm{i}\\ -\mathrm{i}& 0\end{array}\right] \mathrm{and} {\mathrm{A}}^2=\mathrm{KI}$ then K = –1 

Which of the above Statement(s) is true ?

$$\begin{gathered} \left(\mathrm{I}\right): \mathrm{A}=\left[\begin{array}{cc}\mathrm{x}& 1\\ 1& 0\end{array}\right] \\ {\mathrm{A}}^2=\left[\begin{array}{cc}\mathrm{x}& 1\\ 1& 0\end{array}\right] \left[\begin{array}{cc}\mathrm{x}& 1\\ 1& 0\end{array}\right] \\ =\left[\begin{array}{cc}{\mathrm{x}}^2+1& \mathrm{x}\\ \mathrm{x}& 1\end{array}\right] \\ \mathrm{But} {\mathrm{A}}^2=\mathrm{I} \\ \left[\begin{array}{cc}{\mathrm{x}}^2+1& \mathrm{x}\\ \mathrm{x}& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right] \\ \therefore \mathrm{x}=0 \end{gathered}$$

                      $\mathrm{I}$ is correct

$$\begin{gathered} \left(\mathrm{II}\right): {\mathrm{A}}^2=\mathrm{KI} \\ \left[\begin{array}{cc}0& -\mathrm{i}\\ -\mathrm{i}& 0\end{array}\right] \left[\begin{array}{cc}0& -\mathrm{i}\\ -\mathrm{i}& 0\end{array}\right]=\left[\begin{array}{cc}\mathrm{k}& 0\\ 0& \mathrm{k}\end{array}\right] \\ \left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]=\left[\begin{array}{cc}\mathrm{k}& 0\\ 0& \mathrm{k}\end{array}\right] \\ \therefore \mathrm{k}=1 \\ \therefore \left(\mathrm{II}\right) \mathrm{is} \mathrm{correct} \end{gathered}$$