Let $\mathrm{M}=\left(\mathrm{a}_{\mathrm{iij}}\right), \mathrm{i}, \mathrm{j} \in\{1,2,3\}$, be the $3 \times 3$ matrix such that $\mathrm{a}_{\mathrm{ij}}=1$ if $\mathrm{j}+1$ is divisible by i , otherwise $\mathrm{a}_{\mathrm{ij}}=0$. Then which of the following statements is(are) true?
Select ALL correct options:
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
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