Eckmann-Hilton argument

Let $𝑋$ be a set equipped with two binary operations $(\times) : 𝑋 \times 𝑋 \to 𝑋$ and $(\otimes) : 𝑋 \times 𝑋 \to 𝑋$ such that these operations are unital and $(𝑎 \times 𝑏) \otimes (𝑐 \times 𝑑) = (𝑎 \otimes 𝑐) \times (𝑏 \otimes 𝑑)$ for all $𝑎, 𝑏, 𝑐, 𝑑 \in 𝑋$ . Then $(\times) = (\otimes)$ and together with $𝑋$ forms a Commutative monoid. algebra