Automorphisms of quantum matrices

We study the automorphism group of the algebra $\text{oqmn}$ of $n\times n$ generic quantum matrices. We provide evidence for our conjecture that this group is generated by the transposition and the subgroup of those automorphisms acting on the canonical generators of $\text{oqmn}$ by multiplication by scalars. Moreover, we prove this conjecture in the case when $n=3$.