Question

If $A=\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right]$ then $A^{16}$ =

• A. $\left[\begin{array}{cc}0& 256\\ 256& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}256& 0\\ 0& 256\end{array}\right]$
• C. $\left[\begin{array}{cc}-16& 0\\ 0& -16\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 16\\ 16& 0\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}256& 0\\ 0& 256\end{array}\right]$

$A^2=\left[\begin{array}{cc}0& -2\\ 2& 0\end{array}\right],A^4=\left[\begin{array}{cc}-4& 0\\ 0& -4\end{array}\right]A^8=\left[\begin{array}{cc}16& 0\\ 0& 16\end{array}\right],A^{16}=\left[\begin{array}{cc}256& 0\\ 0& 256\end{array}\right]$