Statement-1: Solubility of an amino acid is maximum at isoelectric point. 

Statement-2:  At isoelectric point amino acid exists as zwitter ion.

Protein molecules behave as zwitter ions at the isoelectric point and do not travel in the direction of any electrode or behave as neutral molecules. This minimises their solubility and aids in the separation and purification of the molecules. 1 is therefore untrue.

At a pH equal to the isoelectric point, an amino acid's zwitterion is present. So, 2 is true.