1.2.4 Determinant calculation

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