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Consider the group ${SL}_2\left({\mathbf{O}}_K\right)$ over the ring of algebraic integers of a number field $K$. Define the height of a matrix to be the maximum over all the conjugates of its entries in absolute value. Let ${SL}_2({\mathbf{O}}_K,t)$ be the number of matrices in ${SL}_2\left({\mathbf{O}}_K\right)$ with height bounded by $t$. We determine the asymptotic behaviour of ${SL}_2({\mathbf{O}}_K,t)$ as $t$ goes to infinity including an error term, $${SL}_2({\mathbf{O}}_K,t)=C{t}^{2n}+O\left(t^{2n-\eta }\right)$$ with $n$ being the degree of $K$. The constant $C$ involves the discriminant of $K$, an integral depending only on the signature of $K$, and the value...