Answer
$k=-1$ or $k=4$.
Work Step by Step
A matrix is singular if and only if its determinant is $0$.
We know that for a matrix
$
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
$
the determinant, $D=ad-bc.$
Hence here $D=(k-1)(k-2)-6=0\\k^2-3k+2-6=0\\k^2-3k-4=0\\(k+1)(k-4)=0.$
Thus $k=-1$ or $k=4$.
