A non-magnetic piece of metal can exhibit attraction to a magnet, but it does not possess inherent magnetic properties. The discussion highlights that while the metal is not a magnet itself, it can still be permeable and respond to magnetic fields. When held loosely, the metal tends to flip to one side, suggesting it may have become mildly magnetized. The suggestion to test the metal's magnetism with light ferrous materials, like iron filings, indicates it may have developed some magnetic characteristics. This interaction illustrates the complexities of magnetism and permeability in non-magnetic metals.