   Chapter 11.3, Problem 6E ### 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 = [ 3 2 4 1 1 − 6 2 1 12 ] B = [ 9 − 10 − 8 − 12 14 11 − 1 2 1 2 1 2 ]

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==[39+2(12)+4(12)3(10)+214+4(12)3(8)+211+4(12)19+1(12)+(6)(12)1(10)+114+(6)(12)1(8)+111+(6)(12)29+1(12)+12(12)2(10)+114+12(12)2(8)+111+12(12)]==I

And,

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