1.2.4 Determinant calculation

Problem: Calculate the determinant of a matrix of size $$\times n\left(\begin{array}{cccccc}1& 0& \dots & \dots & 0& 2\\ 0& 1& \dots & \dots & 2& 0\\ \dots & \dots & \dots & \dots & \dots & \dots \\ 0& 2& \dots & \dots & 1& 0\\ 2& 0& \dots & \dots & 0& 1\end{array}\right).$$