Which of the following is false?

Question

Addition is commutative in $\mathbb{N}$.

Multiplication is associative in $\mathbb{N}$.

If $a * b = a^b$ for all $a, b \in \mathbb{N}$, then $*$ is commutative in $\mathbb{N}$.

Addition is associative in $\mathbb{N}$.

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