Question

If $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and A² is the identity matrix, then x = _________________.

Answer 1

The given matrix is $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$.

It is given that, A² = I.

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

Thus, the value of x is 0.

If $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and A² is the identity matrix, then x = ___0___.