Show that the net charge inside the conductor is zero.
depending on your math level, this may help.
https://physics.stackexchange.com/questions/267338/how-to-show-mathematically-that-the-electric-field-inside-a-conductor-is-zero
https://physics.stackexchange.com/questions/267338/how-to-show-mathematically-that-the-electric-field-inside-a-conductor-is-zero