Can an aqueous solution of an ionic material conduct electricity?
Ionic compounds are able to conduct electricity in the aqueous state(that is in solution).
This is because in the aqueous state, the anions and cations are free to move about(unlike in solid where they are fixed).
And so when a pd is applied across it(the ion solution) the anions(-ve) rush to the anode, whereas, the cations(+ve) rush to the cathode
In a melt or in solution.
In an ionic solid the ions are not free to move and are rigidly held in an electrostatic lattice. If we find a solvent to ionize chemically the ionic lattice (water is a good choice), the ions are now free to move and individual ions are solvated by water molecules, and therefore conduct electricity. Likewise, if you pump enough heat in to melt the lattice (and ionic solids such as common salt have exceptionally high melting points), the ions are now free to move and to carry an electrical current.