Answered: Problem 8 §3.7, Exercise 2. Let a 0 be…

Problem 8 §3.7, Exercise 2. Let a 0 be a real number and let A be an invertible matrix. Show that the inverse of the matrix aA is given by A-1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 18E: Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix...

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Problem 8
§3.7, Exercise 2. Let a 0 be a real number and let A be an invertible
matrix. Show that the inverse of the matrix aA is given by A-1.

Expert Solution

Step 1

Given: $α \neq 0$ is a real number and $A$ is an invertible matrix.

To prove: The inverse of the matrix $α A$ is $\frac{1}{α} A^{- 1}$ .

Step by step

Solved in 2 steps

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