Amphoteric Oxides: These are the oxides of elements which are capable of exhibiting both acidic and basic behavior in different reactions.
Well according to IUPAC, only two metal oxides are amphoteric in nature. They are Al₂O₃ and ZnO.
So let us prove Al₂O₃ to be amphoteric. 
Preliminary Needs : Acid + Base => Salt + Water
So Let us take Al₂O₃ to be acidic in nature. Therefore on reacting with acid it will give salt and water as products. So the equation is:
 Al₂O₃ + 2 NaOH + 3 H₂O => 2 NaAl( OH )₄ [ Hydrated form of Al₂O₃ ]
So on reacting NaOH ( Strong Base) with Al₂O₃ we get, Sodium Aluminate as salt and also water as another product.
Now let us take Al₂O₃ to be basic in nature. Then we get an equation as:
6 HCl + Al₂O₃ => 2 AlCl₃ + 3 H₂0
So on reacting HCl ( Strong Acid ) with Al₂O₃, we get Aluminium Chloride as the salt and water as a by product.
Hence the two equation are valid and satisfy the neutralisation reactions respectively.
Hence we can say that, Al₂O₃ is an Amphoteric Oxide.

 

Not all metal oxides are basic some are amphoteric and aluminium oxide is one such example and as Al has diagnoal relation with boron so even boron oxide is basic