   Chapter 11.3, Problem 5E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 3 − 6 ■ Verifying the Inverse of a Matrix: Calculate the products A B and B A to verify that B is the inverse of A . A = [ 1 3 − 1 1 4 0 − 1 − 3 2 ] B = [ 8 − 3 4 − 2 1 − 1 1 0 1 ]

To determine

To find:

The products AB and BA and hence verify that the given matrix B= is inverse of the matrix A=.

Explanation

Approach:

Two matrices A and B can be multiplied if they satisfy the condition that the number of columns in A is same as the number of rows in B.

If A is a square matrix of dimension n×n and there exist another square matrix B of dimension n×n such that AB=I=BA, then we say B is the inverse of A.

Calculation:

AB==[18+3(2)+(1)11(3)+31+(1)014+3(1)+(1)118+4(2)+011(3)+41+0014+4(1)+01(1)8+(3)(2)+21(1)(3)+(3)1+20(1)4+(3)(1)+21]==I

And,

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