Answer
It is a vector space.
Work Step by Step
The set of all $2\times 2$ singular matrices with the standard
operations is a vector space. Since it is closed under addition and scalar multiplication and all other axioms can be shown easily.
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 4 - Vector Spaces - 4.2 Vector Spaces - 4.2 Exercises - Page 160: 29
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