We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the {\em determinant}) over an arbitrary finite field. This answers an open problem of \cite{N91} and \cite{NW95} for the case of finite fields. We intepret here arithmetic circuits in the algebra of polynomials over the given field. The proof method involves a new argument on the rank of linear functions, and a group symmetry on polynomials vanishing at certain nonsingular matrices, and could be of independent interest.