Advanced Engineering Mathematics, 7th Edition

8.5 Properties of Determinants

INTRODUCTION

In this section we are going to consider some of the many properties of determinants. Our goal in the discussion is to use these properties to develop a means of evaluating a determinant that is an alternative to cofactor expansion.

Properties

The first property states that the determinant of an n × n matrix and its transpose are the same.

THEOREM 8.5.1 Determinant of a Transpose

If A^T is the transpose of the n × n matrix A, then det A^T = det A.

For example, for the matrix A = , we have A^T = ...