Help with proving $\mathbb{N} \cong \mathbb{N}^{2}$

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Recently, in an answer to a question I posted on this website, I've been advised to use $\mathbb{N} \cong \mathbb{N}^{2}$. The problem is I haven't been able to prove it, as I've only been able to find injective functions from $\mathbb{N}$ to $\mathbb{N}^{2}$ and have been struggling with finding a bijective one.
Any help with the proof will be much appreciated. Thanks in advance!