Let ***A*** be non singular matrix of order **N** and inverse of ***A*** is known. Is it possible to ***find/approximate*** inverse of ***A*** if only one element of ***A***; **a(i,j)**; is replaced by number approaching infinity(***M*** = big number like 99999999) with less computations.


In this case, **1** row and **1** column of inverse of ***A*** is always **0**.


It is assumed that the other entries of ***A*** are smaller campared to one big entery ***M***.


Thanks.



Inverse of Matrix with one element approches infinity
The inverse of the sum of an invertible matrix and a matrix of rank $1$ can be computed using the [Sherman-Morrison formula](https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula).


