Behaviour of orthogonal matrices

I am given that A is an orthogonal matrix of order $n$, and $u, v$ are Vectors in the $R^n $ space.

I need to prove that $||u|| = ||Au||$. The first step of the solution hint I am given is that $$||Au||^2 = (Au)^T(Au)$$. Why is this so? I know that $A^{-1} = A^T$ in the definition of an orthogonal matrix, but how does this contribute to the above statement? Or is there some other property I’m missing out on?