Matrix model (MM) of SU(2) gauge theory with massless adjoint fermions exhibit \(\mathcal {N}=1\) SUSY with global \(U(1)_R\) symmetry. The quantum mechanical MM provides a simplified framework to numerically study certain interesting aspects of this system. We construct the color-singlet spin-0 and spin-1/2 energy eigenstates using a variational technique and estimate their energies for both weak and strong coupling. At weak coupling ( \(g\le 2\) ), the ground state (GS) is a unique spin-0 state. As g increases, GS exhibit QPT due to level crossing. The system has SUSY in both phases at weak coupling. The excited spin-0 states are super-partners of spin-1/2 energy eigenstates. At strong coupling, GS is 2-fold degenerate (with R = ±1) which breaks \(U(1)_R\) . We explore the fate of SUSY in such a scenario.