Orthogonal transformation of a multivariate normal

Suppose that $X = (X_1, \dots, X_p)^T$ follows $N_p(\mu, \Sigma)$, where $\mu \in \mathbb{R}^p$ and $\Sigma$ is a positive definite matrix. Let $A$ be a $p \times p$ matrix such that $A^T A = I_p$. Let $Y = (Y_1, \dots, Y_p)^T = AX$. Then which of the following statements is/are correct?