Some Java matrix math libraries can do the job. Not every matrix is invertible perhaps you should test if this condition is met.
You probably don't want the inverse. I'm betting that you really want to know how to solve a system of equations. I'd recommend that you look at LU decomposition rather than inverse or Gaussian elimination.It's more stable.
You'll have a hard time inverting a matrix if the determinant of the matrix is zero or VERY small.
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