   Chapter 11.CR, Problem 46E ### 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

# 4 5 − 4 6 . Inverse Matrices: Verify that the matrices A and B are inverses of each other by calculating the products A B and B A . A = [ 2 − 1 3 2 − 2 1 0 1 1 ] , B = [ − 3 2 2 5 2 − 1 1 2 1 − 1 − 1 ]

To determine

To Find:

The products AB and BA and hence verify that the given matrices A= and B= are inverses of each other.

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 B is the inverse of A.

Calculation:

AB==[2(32)+(1)(1)+3122+(1)1+3(1)252+(1)2+3(1)2(32)+(2)(1)+1122+(2)1+1(1)252+(2)2+1(1)0(32)+1(1)+1102+11+1(1)052+12+1(1)]=[3+1+34135233+2+142154101+10+110+21]==I

And,

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