Guided Proof Prove that the determinant of an invertible matrix is equal to if all of

Chapter 3, Problem 55

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Guided Proof Prove that the determinant of an invertible matrix is equal to if all of the entries of and are integers. Getting Started: Denote as and as Note that and are real numbers. To prove that is equal to you must show that both and are integers such that their product is equal to 1. (i) Use the property for the determinant of a matrix product to show that (ii) Use the definition of a determinant and the fact that the entries of and are integers to show that both and are integers. (iii) Conclude that must be either 1 or because these are the only integer solutions to the equation