First column of multicols introduces an unwanted vertical space when first element is displaymath

Code:

\documentclass{article}
\usepackage{multicol}

\begin{document}
\begin{multicols}{3}
$\rho^1 = \left(\begin{array}{ccccc}1&2&3&4&5\\2&4&5&1&3\end{array}\right)$
$\rho^2 = \left(\begin{array}{ccccc}1&2&3&4&5\\4&1&3&2&5\end{array}\right)$
$\rho^3 = \left(\begin{array}{ccccc}1&2&3&4&5\\1&2&5&4&3\end{array}\right)$
$\rho^4 = \left(\begin{array}{ccccc}1&2&3&4&5\\2&4&3&1&5\end{array}\right)$
$\rho^5 = \left(\begin{array}{ccccc}1&2&3&4&5\\4&1&5&2&3\end{array}\right)$
$\rho^6 = \left(\begin{array}{ccccc}1&2&3&4&5\\1&2&3&4&5\end{array}\right)$
\end{multicols}
\end{document}

Output:

Can I remove the vertical space in the first column?

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Using the alignat* environment from »amsmath« might be the better option. – Thorsten Donig Sep 27 '13 at 16:40
@ThorstenDonig That's definitely a better solution, but I am curious as to why the problem exists to begin with. – Sean Allred Sep 27 '13 at 17:00