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You can't share the associative property between the wedge and geometric products like you're doing. The math just doesn't work that way. Here's how to figure out what $\left(e_1\wedge e_2\right)e_1$ and $-e_1 \left(e_1\wedge e_2\right)$ are (and whether they are equal). First off I'm going to assume that $\{e_1, e_2\}$ is an orthonormal basis for $\Bbb ...

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