The number of $3\times 3$ matrices A whose entries are either 0 or 1 and for which the system $A=\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$ has exactly two distinct solution is

Question

$(a)\;0\qquad(b)\;2^9-1\qquad(c)\;168\qquad(d)\;2$