Answer
See below
Work Step by Step
Let $A$ and $B$ be $n \times n$ matrices.
If $A$ is skew-symmetric, then $A^T=-A$
Obtain: $(B^TAB)^T\\=B^TA^T(B^T)^T\\=B^TA^TB\\=B^T(-A)B\\=-(B^TAB)$
Hence, $B^TAB$ is skew-symmetric.
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 2 - Matrices and Systems of Linear Equations - 2.9 Chapter Review - Additional Problems - Page 192: 13
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