  For an arc on a bordered surface with marked points, we associate a holonomy
matrix using a product of elements of the supergroup $\mathrm{OSp}(1|2)$, which
defines a flat $\mathrm{OSp}(1|2)$-connection on the surface. We show that our
matrix formulas of an arc yields its super $\lambda$-length in Penner-Zeitlin's
decorated super Teichm\"uller space. This generalizes the matrix formulas of
Fock-Goncharov and Musiker-Williams. We also prove that our matrix formulas
agree with the combinatorial formulas given in the authors' previous works. As
an application, we use our matrix formula in the case of an annulus to obtain
new results on super Fibonacci numbers.
