   Chapter 11.CR, Problem 9CC ### 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

# (a) What is an identity matrix I n ? If A is an n × n matrix, what are the products A I n and I n A ?(b) If A is an n × n matrix, what is its inverse matrix?(c) Complete the formula for the inverse of a 2 × 2 matrix A = [ a b c d ] (d) Find the inverse of the following matrix. A = [ 1 1 3 − 1 ]

To determine

(a)

The identity matrix In and the products of AIn and InA.

Explanation

Calculation:

The identity matrix In is the n×n matrix for which each main diagonal entry is a 1 and for which all other entries are 0.

Identity matrix In behave like the number 1. Then,

Calculate the product of matrix.

Substitute 1 for In in the product

To determine

(b)

The inverse matrix of A.

To determine

(c)

The formula for the inverse of a 2×2 matrix A.

To determine

(d)

The inverse of matrix A.

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