Geodesic
Automorphisms of the semigroup of nonnegative invertible matrices of order~$2$ over rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 7, pp. 49-60

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In this paper, we describe automorphisms of the semigroup $\mathrm G_2(R)$ of nonnegative invertible matrices if $R$ is a (not necessarily commutative) partially ordered ring without zero divisors with $1/n$ for some natural number $n>1$. 
@article{FPM_2010_16_7_a2,
     author = {E. I. Bunina and L. V. Tupikina},
     title = {Automorphisms of the semigroup of nonnegative invertible matrices of order~$2$ over rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {49--60},
     publisher = {mathdoc},
     volume = {16},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_7_a2/}
}
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E. I. Bunina; L. V. Tupikina. Automorphisms of the semigroup of nonnegative invertible matrices of order~$2$ over rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 7, pp. 49-60. http://geodesic.mathdoc.fr/item/FPM_2010_16_7_a2/