Question

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).