Matrix inversion function correctness issue

At some point in my code I need to invert a series of affine transformation matrices.
I also use dnAnalytics for operations on matrices and solvers. When trying to invert the aforementioned matrices,
the Invert() function of dnAnalytics throws an exception claiming that the matrices are singular.
I converted some matrix to Matrix4d of openTK and called Invert which returned me some result which is definitely wrong since
multiplying with the original matrix does not yield the Identity.
I double checked the matrix with Matlab and indeed it is singular.

I also use OpenTK's Invert to ignore LookAt transformations at some point but it seems to work fine there.
Maybe it is a special case with these matrices but there is a case so I think the inversion algorithm may need some revising.