Question

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$, then $A^4$=__________________

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

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

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

$A^4=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$