The author shows, if \(A\) is a noncentral matrix in the special linear group \(\text{SL}_n(K)\), where \(n>2\) or \(| K|>3\), then every element in \(\text{SL}_n(K)\) is a product of matrices conjugate to \(A\). He gets similar results for the symplectic and for the special orthogonal groups, as well as for semisimple algebraic groups over local fields.