Let A =( x ij), i =1,2,... , k, j =1,2,... , l, 1 ≤ k ≤ l, be a matrix of independent variables, G be the set of maximal minors of A, and I = ( G) be the classical determinantal ideal. We show that G is a universal Gröbner basis of I. Also, a sufficient condition for G to be a universal comprehensive Gröbner basis is proved. Bibliography: 12 titles.