# Unimodular Matrix is a matrix, which has integer entries and determinant of &#x2208;<!-- ∈ -->

Unimodular Matrix is a matrix, which has integer entries and determinant of $\in \left\{+1,-1\right\}$. That means the matrix is invertible over the integers $\mathbb{Z}$.
Given a unimodular matrix A for example:
$\left[\begin{array}{cccccc}2& -2& -5& -4& -2& -3\\ 0& 1& 0& 0& 0& 0\\ -1& 0& 3& 1& -1& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
Need to convert to it to a matrix like this:
$\left[\begin{array}{cccccc}\ast & \ast & \ast & \ast & \ast & \ast \\ \ast & \ast & 0& 0& 0& 0\\ \ast & 0& \ast & 0& 0& 0\\ \ast & 0& 0& \ast & 0& 0\\ \ast & 0& 0& 0& \ast & 0\\ \ast & 0& 0& 0& 0& \ast \end{array}\right]$
where * denotes possible nonzero entries.
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frethi38
The inverse is:
$\left[\begin{array}{cccccc}3& 6& 5& 7& 11& 9\\ 0& 1& 0& 0& 0& 0\\ 1& 2& 2& 2& 4& 3\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
###### Not exactly what you’re looking for?
mravinjakag
The only other idea I have is: if A is unimodular then so is it's inverse, so let $M={A}^{-1}{M}^{\prime }$ where ${M}^{\prime }$ is unimodular of the form you want and chosen such that ${A}^{-1}M$ has the desired first row.