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Another way to see this is by using Pontryagin-Thom. The generator of $\pi_3(S^2)$ is represented by an unlink in $\mathbb{R}^3$ which twists around once (like a figure-8). The generator of $\pi_n(S^n)$ is a disjoint union of $n$ points. This means that postcomposing $\eta$ with an element of $\pi_2(S^2)$ is a disjoint union of n figure-8's, while precomposition with an element of $\pi_3(S^3)$ is cabling the figure-8 n-times. The n-cable of the figure-8 has $n^2$ crossings, so it's cobordant to $n^2$ figure-8s.