I tried this problem but I failed. It is a symmetric matrix, it should be orthogonal diagonalizable. If I can find the eigenvalues and eigenvectors of this matrix, then i can calculate it easily. The answer should be the product of their eigenvalues.
However I am unable to find the eigenvalues since it is a nxn matrix. (I used online calculator to checke, the eigenvalues should be $(n-1)$ times $(x-a)$ and $1 \times [x-(n-1)a]$ May anyone give me any tips on this problem?