The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field

Let $\mathbb F$ be a linearly ordered field. Consider $\mathrm G_n(\mathbb F)$, which is the subsemigroup of $\mathrm{GL}_n(\mathbb F)$ consisting of all matrices with nonnegative coefficients. In 1940, A. I. Maltsev introduced the concept of the group of fractions for a semigroup. In the given paper, we prove that the group of fractions of $\mathrm G_3(\mathbb F)$ coincides with $\mathrm{GL}_3(\mathbb F)$.