= Solution
The <CKM matrix> converts down-type <quark mass> eigenstates into the combinations entering the <weak charged current>. Its entry $V_{ij}$ controls a <weak charged current>[charged-current] transition between up-type <quark flavor>[flavour] $i$ and down-type <quark flavor>[flavour] $j$. In the three-generation <Standard Model>, $V=U_{uL}^\dagger U_{dL}$ is a product of <unitary matrices> from diagonalizing the <quark mass> matrices, so $V^\dagger V=1$.
The <Wolfenstein parametrization> displays the hierarchy
$$
|V|\sim\begin{pmatrix}1&\lambda&\lambda^3\\\lambda&1&\lambda^2\\\lambda^3&\lambda^2&1\end{pmatrix}.
$$
Thus diagonal transitions dominate; first-second generation mixing is larger than second-third generation mixing, and direct first-third generation mixing is smallest. The parameters $A,\rho,\eta$ refine this order estimate. With nondegenerate <quark masses>, a nonzero irreducible weak phase permits <CP violation>; at leading order the <Jarlskog invariant> is $J\simeq A^2\lambda^6\eta$. Individual complex entries are not enough: the phase must survive allowed quark-field rephasings.
The exact physical <CKM matrix> is unitary, whereas its displayed cubic truncation is only approximately so. For example its first-row norm is $1+\lambda^4/4+A^2\lambda^6(\rho^2+\eta^2)$, which is not exactly one for nonzero $\lambda$. The omitted higher-order terms repair this; <unitarity> must be tested to the retained order.
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