Product of two vectors

Question

Let $x, y \in \mathbb{R}^n$, when $x^T y = y^T x$ ?

Answer 1

$x^T y = y^T x$ always. Note that $x^T y$ is a scalar (i.e. a real number), so its transpose is itself ($y^T x = (x^T y)^T = x^T y$).