Problem $4\mathrm{.}1($Matrix multiplications and row$/$column operations$).$ Calculate the following matrix multi$-$

plications

$\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right].$

$\left[\begin{array}{ccc}1& 0& 0\\ -1& 1& 0\\ -1& 0& 1\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 1& 3& 1\\ 1& 4& 0\end{array}\right].$

$\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ -1& 1& 0& 0& 0\\ -1& 0& 1& 0& 0\\ -1& 0& 0& 1& 0\\ -1& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 1& 1& 0& 0& 0\\ 1& 2& 1& 0& 0\\ 1& 3& 3& 1& 0\\ 1& 4& 6& 4& 1\end{array}\right].$

${\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 1& 0& 0& 0\end{array}\right]}^k$

for an integer $k.$ Find the formula depending on $k.$