Let A be a matrix all of whose elements are integers. Show that if IAI = 1, then all the elements of A-1 are integers.

Chapter 1.1 Applications of Linear Equations A strategy for solving applied problems 1. Read the problem as many times as needed to understand it thoroughly. Pay close attention to the question asked to help identify the quantity a variable should represent. 2. Assign a variable to represent the quantity you are looking for and when necessary, express all other unknown quantities in terms of this variable. Frequently, it is helpful to draw a diagram to illustrate the problem or to set up a table to organize the information. 3. Write an equation that describes the situation. 4. Solve the equation. 5. Answer the question asked in the problem. 6. Check the answer against the description of the original problem (not just the equation s