The reason it's a question is because it doesn't say that in the PHB. Everything rules the players need to follow should be in the PHB but it's not. If it was a variant rule sure but a regular common thing for a Wizard to do should be in the PHB. Before we had the DMG and only the PHB there would have been no arcana check.
The PHB is for player knowledge. The DMG is for DM's knowledge. Knowledge of a class belongs to the player. However, knowledge of magic items and how they work belong to the DM.
You can play however you wish though.