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

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

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