Determine the value of kkk such that the matrix A=(1231k312k)A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & k & 3 \\ 1 & 2 & k \end{pmatrix}A=1112k233k is non-invertible.
k=2k = 2k=2 or k=3k = 3k=3
k=1k = 1k=1 or k=2k = 2k=2
k=3k = 3k=3 only
k=0k = 0k=0