MHB Proving Zp is a Vector Space for Prime p

THEcj39
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How can I prove that
Zp is a vector space if and only if p is prime
 
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What does the Z5 under addition and multiplication look like? What are the axioms of vector space?
 
A vector space over what field? Are you sure the problem is not to show that Zp is a field if and only if p prime?
 
Country Boy said:
A vector space over what field? Are you sure the problem is not to show that Zp is a field if and only if p prime?
The exercise doesn't specifies so I think is any field, and yes I'm sure the problem is vector spaces not fields
 
Any field is a vector space over itself so it is sufficient to show that Zp is a field if and only if p is prime.
 

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