Let $M = \left( a _ { i j } \right) , i , j \in \{ 1,2,3 \}$, be the $3 \times 3$ matrix such that $a _ { i j } = 1$ if $j + 1$ is divisible by $i$, otherwise $a _ { i j } = 0$. Then which of the following statements is(are) true?
(A) $M$ is invertible
(B) There exists a nonzero column matrix $\left( \begin{array} { l } a _ { 1 } \\ a _ { 2 } \\ a _ { 3 } \end{array} \right)$ such that $M \left( \begin{array} { l } a _ { 1 } \\ a _ { 2 } \\ a _ { 3 } \end{array} \right) = \left( \begin{array} { l } - a _ { 1 } \\ - a _ { 2 } \\ - a _ { 3 } \end{array} \right)$
(C) The set $\left\{ X \in \mathbb { R } ^ { 3 } : M X = \mathbf { 0 } \right\} \neq \{ \mathbf { 0 } \}$, where $\mathbf { 0 } = \left( \begin{array} { l } 0 \\ 0 \\ 0 \end{array} \right)$
(D) The matrix $( M - 2 I )$ is invertible, where $I$ is the $3 \times 3$ identity matrix