This is a summary of the proof by G.E. Coxson that P-matrix recognition is co-NP-complete. The result follows by a reduction from the MAX CUT problem using results of S. Poljak and J. Rohn.
Cite
@article{arxiv.0710.3519,
title = {P-matrix recognition is co-NP-complete},
author = {Jan Foniok},
journal= {arXiv preprint arXiv:0710.3519},
year = {2007}
}