  Let GL(n,q) be the group of nxn invertible matrices over a field with q
elements, and SL(n,q) be the group of nxn matrices with determinant 1 over a
field with q elements. We prove that the product of any two non-central
conjugacy classes in GL(n,q) is the union of at least q-1 distinct conjugacy
classes, and that the product of any two non-central conjugacy classes in
SL(n,q) is the union of at least $\lceil\frac{q}{2} \rceil$ distinct conjugacy
classes.
