Question: Prove Lemma 4.5. Let B be an n n matrix and let E be an n n elementary matrix. Then det(EB) = (det

Prove Lemma 4.5.

Let B be an n × n matrix and let E be an n × n elementary matrix. Then

det(EB) = (det E) (det B)

We can use Lemma 4.5 to prove the main theorem of this section: a characterization of invertibility in terms of determinants.

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