Advanced Engineering Mathematics, 7th Edition

8.6 Inverse of a Matrix

INTRODUCTION

The concept of the determinant of an n × n, or square, matrix will play an important role in this and the following section.

8.6.1 Finding the Inverse

In the real number system, if a is a nonzero number, then there exists a number b such that ab = ba = 1. The number b is called the multiplicative inverse of the number a and is denoted by a⁻¹. For a square matrix A it is also important to know whether we can find another square matrix B of the same order such that AB = BA = I. We have the following definition.

DEFINITION 8.6.1 Inverse of a Matrix

Let A be an n × n matrix. If there exists an n × n matrix B such that

AB = BA = I, (1)

where I is the n × n identity, then the matrix A is said to be nonsingular ...