If the trace of the matrix $\left(\begin{array}{cccc}1 & a_{12} & \ldots . . & a_{1 n} \\ a_{21} & 2 & \ldots . . & a_{2 n} \\ \cdots . & \ldots . . & \ldots . . & \ldots . . \\ a_{n 1} & a_{n 2} & \ldots . . & n\end{array}\right)$ is 55 then the value of $n$ is
(a) 10
(b) 11
(c) 9
(d) cannot be determined