Question

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$, then which of the following is/are equal to $A^{2020}$

• A. $I$
• B. $O$
• C. $A$
• D. $A^2$

Answer 1

Answer: (A), (D)

$A^2$

$A^2=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=I\therefore A^{2020}=(A^2{)}^{1010}=I^{1010}=I$