A$0$
$D = \left| {\,\begin{array}{*{20}{c}}0&1&{ - 1}\\{ - 1\,\,\,}&0&{\,\,\,2}\\1&{ - 2\,\,\,}&{\,\,\,0}\end{array}\,} \right|\, = \,0$
$D = \left| {\,\begin{array}{*{20}{c}} 1&1&{ - 1}\\ { - 2\,\,\,}&0&{\,\,\,2}\\ 3&{ - 2\,\,\,}&{\,\,\,0} \end{array}\,} \right|\, = \,14 $
$\Rightarrow {D_1} \ne 0$
$D = 0$ and ${D_1} \ne 0,$ hence the system is inconsistent, so it has no solution.