Question

If $A=\left(\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right)$, then $A^4$ is equal to

• A. A
• B. 2A
• C. I
• D. 4A

Answer 1

Answer: (C)

$A^2=\left(\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right)\left(\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right)=I$
$\therefore A^4={\left(A^2\right)}^2=I^2=I$