Is there a quick way to invert the $n\times n$ Vandermonde matrix with columns $(1, x, x^2, ..., x^{n-1})$ where $x$ takes values $0,1,...,n-1$ (in ascending order from left to right)?
Perhaps by row operations $(A|I)\to (I|A^{-1})$ where $A$ is the Vandermonde matrix, and $I$ the identity matrix? I don't see how to do it though... or maybe there is another way?
Thank you.