1.4.1 Matrix transformations

Problem: Find inverse matrix to matrix \( A \) of size \( \times n \) \[ \left(\begin{array}{cccccc} n & n-1 & n-2 & \ldots & 2 & 1 \\ 1 & n-1 & n-2 & \ldots & 2 & 1 \\ 1 & 1 & n-2 & \ldots & 2 & 1 \\ \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\ 1 & 1 & 1 & \ldots & 2 & 1 \\ 1 & 1 & 1 & \ldots & 1 & 1 \end{array}\right) . \]