Looking at page 11 of the text, consider a Galois representation $\rho: G_{\mathbb Q} \to \operatorname{GL}_2(A)$, where $A$ is a coefficient ring (i.e. complete Noetherian local ring with finite residue field $k$ of characteristic $p$). We say $\rho$ is ordinary at $p$ if, after suitable choice of basis,
$$\rho|_{I_p} = \begin{pmatrix} \chi_p & * \\ 0 & 1 \end{pmatrix}$$
where $I_p$ is the inertia group at $p$ and $\chi_p$ is the $p$-adic cyclotomic character (or the mod $p$ cyclotomic character if we are considering $\rho_0: G_{\mathbb Q} \to \operatorname{GL}_2(k)$).
At the bottom of the page, the author claims that if $\rho_0$ is ordinary at $p$, then any type $D$ deformation $\rho$ of $\rho_0$ associated to a finite set of primes $D$ (see the bottom of page 11 for a brief explanation of this terminology) is also ordinary at $p$. Why is this true?
