A Laplace expansion along the first row gives
[tex]\begin{vmatrix}1&4&4\\5&2&1\\1&5&5\end{vmatrix}=1\begin{vmatrix}2&1\\5&5\end{vmatrix}-4\begin{vmatrix}5&1\\1&5\end{vmatrix}+4\begin{vmatrix}5&2\\1&5\end{vmatrix}[/tex]
[tex]=1(10-5)-4(25-1)+4(25-2)[/tex]
[tex]=1[/tex]
