Let \( M=(a_{ij}),\, i,j\in\{1,2,3\} \), be the \( 3\times3 \) matrix such that \( a_{ij}=1 \) if \( j+1 \) is divisible by \( i \), otherwise \( a_{ij}=0 \). Then which of the following statements is(are) true?
\( M \) is invertible
There exists a nonzero column matrix
The set \( \{X\in\mathbb{R}^{3}:MX=0\}\neq\{0\} \), where
The matrix \( (M-2I) \) is invertible, where \( I \) is the \( 3\times3 \) identity matrix
