Why is <n|n-2> equal to 0 in computing <n|\hat{a}^2|n>?

[Kidiz]

Homework Statement

This is not really homework. I'm just studying and came across this question. So, I'm not sure if I should post this question here on one of the physics sections.

On computing $<n|\hat{a}^2|n>$, one arrives at $\sqrt{n}*\sqrt{n-1}<n|n-2>=0$ because $<n|n-2>=0$

Now, why is that so?

 

[Fightfish]

Isn't that just because the two Fock states are orthogonal?