Let `M = (a_(ij)) , i , j in {1,2,3}`, be the `3 xx 3` 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 ?

Options

A. M is invertible
B. There exists a nonzero column matrix `((a_1),(a_2),(a_3))` such that `M((a_1),(a_2),(a_3))=((-a_1),(-a_2),(-a_3))`
C. The set `{X in RR^3 :MX=0} ne {0}`, where `0=((0),(0),(0))`
D. The matrix `(M-2I)` is invertible, where `I` is the `3 xx 3` identity matrix