Answer
See proof below.
Work Step by Step
Since $A$ and $B$ are skew-symmetric matrices, then $A^{T}=-A$ and $B^{T}=-B$
Thus
$(A+B)^{T}=A^{T}+B^{T}=-A+(-B)=(-1)A+(-1)*B=(-1) * (A+B)=-(A+B)$
and $A+B$ is a skew-symmetric matrix.
Elementary Linear Algebra 7th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
1-13311-087-8
ISBN 13:
978-1-13311-087-3
Chapter 2 - Matrices - 2.2 Properties of Matrix Operations - 2.2 Exercises - Page 61: 72
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