Answer
$\det (AB^T)=15$
Work Step by Step
Applying Theorem 3.2.5, we have:
$\det (AB^T)=\det (A).\det (B^T)$
Determinant of $B^T$ can be evaluate by the property P5:
$\det (B^T)=\det (B)=3$
Hence, $\det (AB^T)=5.3=15$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 3 - Determinants - 3.2 Properties of Determinants - Problems - Page 220: 37
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