Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 4 - Eigenvalues and Eigenvectors - 4.2 Determinants - Exercises 4.2 - Page 282: 52



Work Step by Step

We know that if $A$ and $B$ are $n\times n$ matrices, then $det(AB)=det(A)det(B)$. We also know that if $A$ is invertible, then $det(A^{-1})=\frac{1}{det(A)}$ We also know that if $A$ is an $n\times n$ matrix, then $det(kA)=k^ndet(A)$ We also know that if $A$ is a square matrix, then $det(A^T)=det(A)$ Hence $det(AA^T)=det(A)det(A^T)=det(A)det(A)=3\cdot3=9$
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