  Matrix inflation, or M-flation, is a string theory motivated inflationary
model with three scalar field matrices and gauge fields in the adjoint
representation of the $\mathbf{U}(N)$ gauge group. One of these $3N^2$ scalars
appears as the effective inflaton while the rest of the fields (scalar and
gauge fields) can play the role of isocurvature fields during inflation and
preheat fields afterwards. There is a region in parameter space and initial
field values, "the hilltop region," where predictions of the model are quite
compatible with the recent Planck data. We show that in this hilltop region, if
the inflaton ends up in the supersymmetric vacuum, the model can have an
embedded preheating mechanism. Couplings of the preheat modes are related to
the inflaton self-couplings and therefore are known from the CMB data. Through
lattice simulations performed using a symplectic integrator, we numerically
compute the power spectra of gravitational waves produced during the preheating
stage following M-flation. The preliminary numerical simulation of the spectrum
from multi-preheat fields peaks in the GHz band with an amplitude
$\Omega_{\mathrm{gw}}h^{2} \propto 10^{-16}$, suggesting that the model has
concrete predictions for the ultra-high frequency gravity-wave probes. This
signature could be used to distinguish the model from rival inflationary models
