Well I didn't know how to write the whole thing so I added a picture instead. By the way, I tried this question several times by finding a sequence in the multiples of $M$ but I haven't got any grasp on it as I am having trouble with $Q$, As said in the question it is a matrix made from summation of GP of matrix $M$ but in the options $Q$ is a value which is possible only if it is a determinant. Anyway I am totally confused with the question, some useful insights would be very useful.
Thanks guys
(A) is right.
Since for any $k$ the matrix $M_3^k$ will have $1$'s on its main diagonal, so $Q$ will have $50$'s on its main diagonal, which means that
$1^{50}+\omega^{50}+(\omega^2)^{50} =1 + \omega^{48}\omega^2 +\omega^{99}\omega= 1+\omega +\omega^2 =0$
Also note that $$M_3^k= \begin{pmatrix} 1 & k & (a_{3,3})_{k-1}+k \\ 0 & 1 & k \\ 0 & 0 & 1 \end{pmatrix}$$
Where $(a_{3,3})_{k-1}$ is the $(3,3)$ entry in the matrix $M_3^{k-1}$