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Linear Algebra With Applications
Found in: Page 309
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

If all the entries of an invertible matrix A are integers, then the entries of A-1 must be integers as well.

The given statement is false.

See the step by step solution

Step by Step Solution

Step 1: Matrix Definition

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “ m by n ” matrix, written “ m×n .”

Step 2: To check whether the given condition is true or false

To find A-1 :

For example,

A=1211 is an invertible matrix with all integer entries.

By using A-1 formula, however


Therefore, the A and A-1 both are different.

So, the given statement is false.

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