Hi, there

I have looked it up in the current textbook. The conventional numerical method to compute the inversion of an $n \times n$ matrix requires $O(n^3)$. However, for the following special matrix ${(E-a \cdot X)}^{-1}$, where $E$ is an $n \times n$ identity matrix, $0 < a < 1$ is a scalar, and $X$ is a stochastic matrix (the sum of each row is 1, and all its entries are between 0 and 1). Then do you have some ideas to compute ${(E-a \cdot X)}^{-1}$ as fast as you can? Thanks in advance!