An expression for the electrical conductivity at the core of a magnetar is derived using Boltzmann kinetic equation with the relaxation time approximation. The rates for the relevant scattering processes, e.g., electron-electron and electron-proton are evaluated in presence of strong quantizing magnetic fields using tree level diagrams. It is found that in presence of a strong quantizing magnetic field, electrical conductivity behaves like a second rank tensor. However, if the zeroth Landau

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... ls are only occupied by the charged particles, it again behaves like a scaler of a one dimensional system.