1.2.5 Determinant calculation

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