  We propose Wronskian-like determinant formulae for the Baxter Q-functions and
the eigenvalues of transfer matrices for spin chains related to the quantum
affine superalgebra U_{q}(hat{gl}(M|N)). In contrast to the supersymmetric
Bazhanov-Reshetikhin formula (the quantum supersymmetric Jacobi-Trudi formula)
proposed in [Z. Tsuboi, J. Phys. A: Math. Gen. 30 (1997) 7975], the size of the
matrices of these Wronskian-like formulae is less than or equal to M+N. Base on
these formulae, we give new expressions of the solutions of the T-system
(fusion relations for transfer matrices) for supersymmetric spin chains
proposed in the abovementioned paper. Baxter equations also follow from the
Wronskian-like formulae. They are finite order linear difference equations with
respect to the Baxter Q-functions. Moreover, the Wronskian-like formulae also
explicitly solve the functional relations for Backlund flows proposed in [V.
Kazakov, A. Sorin, A. Zabrodin, Nucl. Phys. B790 (2008) 345
[arXiv:hep-th/0703147]].
