Linear Algebra

Which of the following statements are TRUE for an $n \times n$ real orthogonal matrix $Q$?

Options:

• (A) The columns of $Q$ form an orthonormal basis of $\mathbb{R}^n$
• (B) $\|Q x\| = \|x\|$ for all $x \in \mathbb{R}^n$
• (C) All eigenvalues $\lambda$ satisfy $|\lambda| = 1$
• (D) $Q^{-1} = Q^T$