$E$ in a solid uniformly charged conductor: Is my reasoning here correct?

Suppose we take spherical conductor which is having both positive and negative charges but as a whole is electrically uncharged and is not under the influence of any external Electric field, We can say that the E outside the conductor is zero by gauss law if take the gaussian surface outside the solid conductor as q enclosed by the gaussian surface is zero. But if I take the gaussian surface inside the conductor which is centered around the center of the conductor the q enclosed by that gaussian surface would still be zero as the enclosed volume still has equal positive and negative charges and hence the net enclosed charge is zero and hence E (electric field) inside the conductor is zero. If the conductor is composed of only positive or negative charges then there will be E inside the conductor as q enclosed in this case by a gaussian surface would not be zero as the conductor contains only 1 type of charge. the value of this electric field can easily be calculated by using the gauss law.