How do I reduce this matrix to row echelon form and hence find the determinant, or is there a way that I am unaware of that finds the determinant of this matrix without having to reduce it row echelon form given this is all I know and there exists no additional information.
$\left[ \begin{array}{ccc} a & 1 & -1 \\ a & 2a+2 & a \\ a-3 & a-3 & a-3 \\ \end{array} \right]$