Clear["`*"]
k1a1=kx;
k2a2=kx/2+ky*Sqrt[3]/2;
k3a3=-kx/2+ky*Sqrt[3]/2;
H=-2*t*({{0,Cos[k1a1],Cos[k2a2]},{Cos[k1a1],0,Cos[k3a3]},{Cos[k2a2],Cos[k3a3],0}});
MatrixForm[H]
eigenvalue=MatrixForm[Eigenvalues[H]]