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a. Suppose A is an n n matrix with integer entries and det A = 1. Show that A 1 has all

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams ISBN: 9781429215213 438

Solution for problem 7 Chapter 5.2

Linear Algebra: A Geometric Approach | 2nd Edition

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Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

Linear Algebra: A Geometric Approach | 2nd Edition

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Problem 7

a. Suppose A is an n n matrix with integer entries and det A = 1. Show that A 1 has all integer entries. b. Conversely, suppose A and A 1 are both matrices with integer entries. Prove that det A = 1.

Step-by-Step Solution:
Step 1 of 3

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Step 2 of 3

Chapter 5.2, Problem 7 is Solved
Step 3 of 3

Textbook: Linear Algebra: A Geometric Approach
Edition: 2
Author: Ted Shifrin, Malcolm Adams
ISBN: 9781429215213

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a. Suppose A is an n n matrix with integer entries and det A = 1. Show that A 1 has all