Power of a non upper triangular matrix be upper triangular

Question

Can the $n-$th power of a non-upper triangular matrix be an upper triangular matrix?

Answer 1

$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\\$$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\\$=$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\\$

Answer 2

Let $A=\left[ \begin{matrix} 0 & 0 \\ 1& 0 \end{matrix} \right].$