Let A be an invertible matrix. Show that (An)?l = (A?1) n

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

ISBN: 9780073383095 37

Solution for problem 21E Chapter 2.6

Discrete Mathematics and Its Applications | 7th Edition

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Problem 21E

Let A be an invertible matrix. Show that (An)‒l = (A‒1) n whenever n is a positive integer.

Step-by-Step Solution:

Solution

In this question we have to prove that $({A}^{n}{)}^{-1}=({A}^{-1}{)}^{n}$ .

Step 1

Taking Left hand side (L.H.S)

$({A}^{n}{)}^{-1}$

Put $n=1$ we get ,

$({A}^{1}{)}^{-1}$

=> ${A}^{-1}$

Now, taking right hand side (R.H.S)

$({A}^{-1}{)}^{n}$

Put $n=1$ we get ,

$({A}^{-1}{)}^{1}$

=> ${A}^{-1}$

So, L.H.S = R.H.S

Step 2 of 2

Chapter 2.6, Problem 21E is Solved

Textbook: Discrete Mathematics and Its Applications

Edition: 7

Author: Kenneth Rosen

ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “Let A be an invertible matrix. Show that (An)?l = (A?1) n whenever n is a positive integer.” is broken down into a number of easy to follow steps, and 18 words. The full step-by-step solution to problem: 21E from chapter: 2.6 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Since the solution to 21E from 2.6 chapter was answered, more than 398 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Integer, invertible, let, Matrix, Positive. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.