Decomposition of matrices from $S{L}_2(K[x,y])$

Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and $\mathbb{K}[x,y]$ the polynomial ring. The group ${\text{SL}}_2(\mathbb{K}[x,y])$ of all matrices with determinant equal to $1$ over $\mathbb{K}[x,y]$ can not be generated by elementary matrices. The known counterexample was pointed out by P.M. Cohn. Conversely, A.A.Suslin proved that the group ${\text{SL}}_r(\mathbb{K}[x_1,\dots ,x_n])$ is generated by elementary matrices for $r\ge 3$ and arbitrary $n\ge 2$, the same is true for $n=1$ and arbitrary $r\mathrm{.}$ It is proven that any matrix from ${\text{SL}}_2(\mathbb{K}[x,y])$ with at least one entry of degree $\le 2$ is either a product of elementary matrices or a product of elementary matrices and of a matrix similar to the one pointed out by P. Cohn. For any matrix $\left(\begin{array}{c}\begin{array}{cc}f& g\\ -Q& P\end{array}\end{array}\right)\in {\text{SL}}_2(\mathbb{K}[x,y])$, we obtain formulas for the homogeneous components $P_i,Q_i$ for the unimodular row $(-Q,P)$ as combinations of homogeneous components of the polynomials $f,g,$ respectively, with the same coefficients.