Answer
9
Work Step by Step
If A and B are $n×n$ matrices, then:
$\det(AB)=\det(A).\det(B)$
Also: $\det(A^T)=\det(A)$
Hence here,
$\det(B^{-1}AB)^2=\det(A).\det(B)=[\frac{1}{\det(B)}\det(A).\det(B)]^2=[\frac{1}{-4}.3.(-4)]^2=3^2=9$
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 - 3.4 Summary of Determinants - Problems - Page 241: 27
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