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Let m, n be positive integers or monic polynomials in mb F_{q}[T] with n | m.Let K_m and K_m^+ be the m-th cyclotomic field and its maximal real subfield, respectively.In this paper we define two matrices mc D_{m,n}^+ and mc D_{m,n}^-whose determinants give us the ratios frac{h(mc O_{K_m^+})}{h(mc O_{K_n^+})}and frac{h^{-}(mc O_{K_m})}{h^{-}(mc O_{K_n})} with some factors, respectively.