SU(2) gauge theory coupled to Weyl fermions of two flavors, has \(SU(2)_B \times U(1)_R\) global symmetry. In this model, there is a long-standing debate whether the low-energy dynamics is confining with spontaneously broken \(SU(2)_B\) . The multiple lattice QCD simulations and theoretical studies suggest that \(SU(2)_B\) -symmetry remains unbroken in the strong coupling regime. Here, we consider a matrix model of 2-color 2-flavor adjoint-QCD(QCD \(_{2,2}\) ). We find that in the extremely strong coupling limit \(U(1)_R\) is broken to \(\mathbb {Z}_4\) and \(SU(2)_B\) symmetry remains unbroken. If we include a chiral chemical potential term to the Hamiltonian, the system undergoes one or two quantum phase transitions(QPTs). For weaker coupling, there are two QPTs separating three distinct phases and one of this phases breaks \(SU(2)_B\) -symmetry spontaneously.