4 (10) Let \( A \in M_{n \times n}(\mathbb{R}) \) and \( r \in \mathbb{R} \). Suppose \( A - rI_n = QR \) where \( Q \) is orthogonal and \( R \) is upper-triangular. Let \( B = RQ + rI_n \). Show that \( A \) and \( B \) have the same eigenvalues.