I have not been able to find any LAPACK libraries for C++ AMP. However, there are some available for OpenCL.
Specifically clMAGMA from the University of Tennessee.
http://icl.cs.utk.edu/magma/software/view.html?id=152
You will need the AMD OpenCL BLAS library to sit under the LAPACK from here:
http://developer.amd.com/tools-and-sdks/heterogeneous-computing/amd-accelerated-parallel-processing-math-libraries/
I think this is your only bet at inverting a matrix with open source libraries on your GPU. Being openCL, this will be platform agnostic (like C++ AMP), unlike CUDA.
-Matt Musto
www.mustotechnologies.com