The matrix elements of a 2 – D electron gas restricted in a GaAs cylindrical quantum wire including Rashba Spin Orbit Interaction, under simultaneous effect of hydrostatic pressure and temperature is investigated. The strong dependency of hydrostatic pressure and absolute temperature, on energy band gap and effective mass of charge carriers of the quantum wire, have been found. Because of this, the linear and non-linear properties of the quantum wire also get affected. We also observed that under the influence of electric and mamagnetic field, the matrix elements get affected strongly with the change in Rashba spin orbit interaction and Magnetic field.