True or false, with reason if true or counterexample if false: (1) If A is invertible

Chapter 1, Problem 1.12

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True or false, with reason if true or counterexample if false: (1) If A is invertible and its rows are in reverse order in B, then B is invertible. (2) If A and B are symmetric then AB is symmetric. (3) If A and B are invertible then BA is invertible. (4) Every nonsingular matrix can be factored into the product A = LU of a lower triangular L and an upper triangular U.

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