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Let $A: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ and $B: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$, so $B A: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ and $A B: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$.
a) Show that $B A$ can not be invertible.
b) Give an example showing that $A B$ might be invertible (in this case it usually is).
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