I need to explain why V is not a vector space over F with respect to the given operations below. I just need to flag one space axiom that fails. In the case below, I cannot find any failing axioms and wonder if it is a trick question, or just erroneous question. V=M2x3(R), F=M2x2(R), the usual matrix addition and matrix multiplication.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
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I need to explain why V is not a vector space over F with respect to the given operations below. I just need to flag one space axiom that fails. In the case below, I cannot find any failing axioms and wonder if it is a trick question, or just erroneous question.

V=M2x3(R), F=M2x2(R), the usual matrix addition and matrix multiplication.

 

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