Let $A$ be a square matrix such that $a_{i,j}=|j-i|$, show that the determinant is $D_n=(-1)^{n-1}(n-1)2^{n-2}$
I have been struggling with this problem for a while now and I was hoping to get the slightest of nudges towards the solution. I would appreciate it if you phrase your hints in forms of questions so I can work through the idea. Please don't post a complete solution unless I asked, and thank you for your time. I wanted to obtain a recurrence relation between $D_n$ and $D_{n-1}$ but I failed. So far, I attempted to use Gaussian elimination on the first and last row and I obtained $(-1,1,\ldots,1)$ and $(1,1,\ldots,-1)$ for the first and last row respectively but I didn't know how to proceed from then on.