Lemma 59.61.2. Let $A$ be a finite central simple algebra over $K$. Then

\[ \begin{matrix} A \otimes _ K A^{opp}
& \longrightarrow
& \text{End}_ K(A)
\\ \ a \otimes a'
& \longmapsto
& (x \mapsto a x a')
\end{matrix} \]

is an isomorphism of algebras over $K$.

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