  In this thesis, we studied the bosonic BFSS and IKKT matrix models using
Monte Carlo simulations. First, we explored some toy models to check the
validity of the numerical simulations. Then we simulated the BFSS matrix model
using Hamiltonian Monte Carlo (HMC) algorithm. In the BFSS matrix model, we
used the Polyakov loop as an order parameter to investigate the large-N
behaviour of this model at different temperatures. Our simulations confirmed
that the model exhibits a confinement-deconfinement phase transition as the
temperature of the system is varied. Besides the Polyakov loop, other
observables such as internal energy and extent of space were also computed. In
the bosonic IKKT model, we studied the spontaneous symmetry breaking (SSB) of
SO(10) symmetry using the moment of inertia tensor and found that there is no
SSB of SO(10) symmetry in this model. Besides the eigenvalues of the moment of
inertia tensor, other observable such as extent of spacetime was also computed.
We also studied the simulation theory of the phase-quenched IKKT model.
