Matrix inverse - measure of approximation

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I have a matrix, if I apply inverse function from existing softwares, I get an inverse matrix for every non singular matrix.

I would like to know if there is a measure that tells that how close the approximation to check weather to consider the inverse matrix not.

In my application, there is a possibility to discard an inverse matrix that's not well approximated.

I am looking for few hints, keywords to look for or an advice in calculating the measure.

I really appreciate any kind of help.