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What use is the inverse matrix? I would not use it to solve linear systems but there must be some concrete or real life applications where it is used.

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    Why wouldn't you use it to solve linear systems? I imagine it's certainly the best way for a computer to solve a linear system, even in cases where a human could "just see" the answer faster than compute the inverse of a matrix.2012-06-07
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    @Matt, [computing the inverse isn't actually the best way for a computer to solve a linear system](http://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/).2012-06-07
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    @RahulNarain That is surprising and interesting, thanks!2012-06-07
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    If you have a matrix $A$ of a linear transformation $f$ in a certain basis, and then you want to work with a different basis, you would use some matrix $X$ and its inverse to compute the new matrix representation of $f$ in the new basis.2012-06-07

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