[Math] Inverse of an upper triangular matrix with all entries 1

Question

I want to find the inverse of a large upper triangular matrix where all its entries are 1.

Is there some trick to it or do I have to compute it using the usual way?

Answer 1

What about $$\left[\begin{array}{ccccccc} 1 & -1 & 0 & 0 & 0&\dots\\ 0 & 1 & -1 & 0&0&\dots\\ 0 & 0 & 1 & -1 & 0&\dots\\ 0 & 0 & 0 & 1 & -1 &\dots\\ 0 & 0 & 0 & 0 & 1 & \dots\\ \vdots & \vdots & \vdots & \vdots & \vdots &\ddots \end{array}\right]$$