The la4j library (Linear Algebra for Java) supports matrix inversion. Here is a quick example:
Matrix a = new Basic2DMatrix(new double[][]{
{ 1.0, 2.0, 3.0 },
{ 4.0, 5.0, 6.0 },
{ 7.0, 8.0. 9.0 }
});
Matrix b = a.invert(Matrices.DEFAULT_INVERTOR);
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