1.5.2 A theorem of l. algebra states that if A and B are invertible matrices, then AB is invertible

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Problem 1.5.2 From Smith/Eggen's A Transition to Advanced Mathematics 7th edition from chapter 1, logic and proofs - basic proof methods II.
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A theorem of linear algebra states that if A and B are invertible matrices, then
the product AB is invertible. As in Exercise 1,
(a) outline a proof of the theorem by contraposition.
(b) outline a proof of the converse of the theorem by contraposition.
(c) outline a proof of the theorem by contradiction.
(d) outline a proof of the converse of the theorem by contradiction.
(e) outline a two-part proof that A and B are invertible matrices if and only
if the product AB is invertible.

Sofia Veloso Magioli e Mello

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