Question

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],$ then $A^2$ is equal to

• A. $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 0\\ 1& 0\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 1\\ 0& 1\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

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