An associative k-algebra whose enveloping algebra $A \otimes_k A^{op}$ is not iso to $A \otimes_k A$

Question

I'm trying to find an example of a finite-dimensional $k$-algebra $A$ for some field $k$, ideally $\mathbb R$, such that $A \otimes_k A \not\cong A \otimes_k A^{op}$.

A lot of algebras have $A \cong A^{op}$, including square matrices and Clifford algebras. A counterexample is for instance when $A$ is path algebra of the quiver $\bullet \rightarrow \bullet \leftarrow \bullet$. But does that produce an example?