Change font color of a column in a matrix

If you want to automate this process for an entire column, then you need to have access to the column specification. This is not possible via amsmath's *matrix environments. Instead, use array and insert \color{red} in front of every entry using the >{<prefix>} specification:

\documentclass{article}

\usepackage{amsmath,array,xcolor}

\begin{document}

$
  A = \begin{bmatrix}
    a & b & c & d \\
    a & b & c & d \\
    a & b & c & d \\
    a & b & c & d
  \end{bmatrix} \qquad
  \left[\begin{array}{@{} >{\color{red}}c c >{\color{red}}c c @{}}
    a & b & c & d \\
    a & b & c & d \\
    a & b & c & d \\
    a & b & c & d
  \end{array}\right] = A
$

\end{document}

A Little bit easier!

\documentclass[a4paper,11pt]{article}

\usepackage{amsmath}
\usepackage{color}

\begin{document}

\[
A =
\def\b{b}
\def\d{d}
\def\a{\color{red}a}
\def\c{\color{red}c}
\begin{bmatrix}
\a & \b & \c & \d \\
\a & \b & \c & \d \\
\a & \b & \c & \d \\
\a & \b & \c & \d \\
\end{bmatrix}
\]

\end{document}