Is the Cabibbo-Kobayashi-Maskawa matrix symmetric?

We examine some of the consequences of having a Cabibbo-Kobayashi-Maskawa (CKM) matrix V with symmetric moduli. We define an asymmetry parameter for a three-generation CKM matrix which can be simply expressed in terms of the eigenstates and the eigenvalues of V. The fact that experimentally the asymmetry is small implies that two of the eigenvalues of V are almost degenerate and/or the eigenstates of V are close to being real. We point out that it is a special feature of three generations that a symmetric ‖V‖ implies that V can be made symmetric by appropriate choice of quark field phases. We analyze a recent ansatz by Kielanowski which leads to a symmetric CKM matrix. A simple parametrization for a symmetric CKM matrix is presented and consequences for the top-quark mass and the ratio ‖${\mathit{V}}_{\mathit{u}\mathit{b}}$‖/‖${\mathit{V}}_{\mathit{c}\mathit{b}}$‖ are examined.