As Jason mentioned, this seems to work fine. For instance:
var y = Complex32.ImaginaryOne * CreateMatrix.Dense(4, 4, new Complex32[] {-13f,5f,4f,0f,5f,-13.5f,2.5f,2f,4f,2.5f,-9f,2.5f,0f,2f,2.5f,-4.5f}); y.ToString("F3"); y.Inverse().ToString("F3");
Provides the following result that matches your book result (except for poor rounding in the book):
DenseMatrix 4x4-Complex32 (0.000, -13.000) (0.000, 5.000) (0.000, 4.000) (0.000, 0.000) (0.000, 5.000) (0.000, -13.500) (0.000, 2.500) (0.000, 2.000) (0.000, 4.000) (0.000, 2.500) (0.000, -9.000) (0.000, 2.500) (0.000, 0.000) (0.000, 2.000) (0.000, 2.500) (0.000, -4.500) DenseMatrix 4x4-Complex32 (0.000, 0.153) (0.000, 0.097) (0.000, 0.126) (0.000, 0.113) (0.000, 0.097) (0.000, 0.153) (0.000, 0.124) (0.000, 0.137) (0.000, 0.126) (0.000, 0.124) (0.000, 0.256) (0.000, 0.197) (0.000, 0.113) (0.000, 0.137) (0.000, 0.197) (0.000, 0.393)