We cant follow conventional steps here due to time factor but if i would have to ans it quickly then i will go with OPTION B bcz
we have equation for the characteristic polynomial of a 
matrix
and for 3*3 matrix
P3(x)=x3 - x2[Tr(A)] + x[A11+A22+A33] - det(A)
Where A11,A22,A33 are sum of minors of diagonal elements.
Analyze here each time the series is increment by one term and it contains trace and determinant.
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In any characteristics equations we need det(A) and clearly det(A)=0 here bcz here identical rows/cols are present so except B all options are wrong here bcz those options still contain 5 terms which infers presence of Determinant.
PS:-Here Sum of Minors of diagonal elements also 0.
