2 of 3 Fixed markdown

Here is an option using kbordermatrix:

enter image description here

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{kbordermatrix}% http://www.hss.caltech.edu/~kcb/TeX/kbordermatrix.sty
\begin{document}
\[
  \begin{array}{l@{{}={}}c}
  \text{Mat}_{\varphi\text{ to }M} & \left(\begin{array}{@{}ccccc@{}}
    1 & 1 & 1 & 1 & 1 \\
    0 & 1 & 0 & 0 & 1 \\
    0 & 0 & 1 & 0 & 1 \\
    0 & 0 & 0 & 1 & 1 \\
    0 & 0 & 0 & 0 & 1
  \end{array}\right)
  \end{array}
\]

\renewcommand{\kbldelim}{(}% Left delimiter
\renewcommand{\kbrdelim}{)}% Right delimiter
\[
  \text{Mat}_{\varphi\text{ to }M} = \kbordermatrix{
    & c_1 & c_2 & c_3 & c_4 & c_5 \\
    r_1 & 1 & 1 & 1 & 1 & 1 \\
    r_2 & 0 & 1 & 0 & 0 & 1 \\
    r_3 & 0 & 0 & 1 & 0 & 1 \\
    r_4 & 0 & 0 & 0 & 1 & 1 \\
    r_5 & 0 & 0 & 0 & 0 & 1
  }
\]

\end{document}

For more options and styles, including the usage of \bordermatrix, see Where is the \matrix command?