The expectation of the product of an estimator with its transpose

Question

I hope you are well. I have a problem that it seems to be really easy but I just don't know how to find the solution. So, this is the question ; I have to compute E(Ŷ'Ŷ). For that, I have some informations to use (I will show some formulas and the β is an estimator, I just don't know how to put an accent on it, sorry...) :

1. Ŷ = X β
2. β = ((X ′ X)^(-1)) X ′ Y
3. the properties of the trace : tr(ab) = tr(ba)

And I have to find something with E(Ŷ'Ŷ), a solution but I just don't know what ... can someone please help me?