Answer
$k=-3$ or $k=2$.
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 $D=(k-1)(k+2)-4=0\\k^2+k-2-4=0\\k^2+k-6=0\\(k+3)(k-2)=0.$
Thus $k=-3$ or $k=2$.
