14. Find the determinant and characteristic roots of the matrix A where

$$A = \begin{bmatrix} 0 & 1 & 1 & ... & 1 \\ 1 & 0 & 1 & ... & 1 \\ 1 & 1 & 0 & ... & 1 \\ . & . & . & ... & . \\ 1 & 1 & 1 & ... & 0 \end{bmatrix}$$

each identity has size k x k, and there are n² submatrices.