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The number of $$3\times3$$ matrices A whose entries are either O 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 solutions, is
$$0$$
$$2^{9}-1$$
$$168$$
$$2$$
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