I tried finding the solution by assuming i and j are both n, but I'm not sure if this is the proper direction to go.
closed as off-topic by Leucippus, Shailesh, Cesareo, Lee David Chung Lin, Saad Mar 15 at 0:48
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Hint: the first column is $\mathbf v=(2,3,\dots,n)^T$. Furthermore, the $i$th column is given by $\mathbf v+(i-1)\mathbf 1$ where $\mathbf 1\in\mathbb R^n$ is the vector whose entries are all $1$s. What does this tell you about the number of column vectors of the matrix that are linearly independent?