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Homework Statement
The set of all nonsingular 3x3 matrices does not form a vector space over the real numbers under addition. Why?
Homework Equations
A vector space over F, under addition, is a nonempty set V such that
A1 Addition is associative
A2 Existence of 0
A3 Existence of negative
A4 Addition is commutative
The Attempt at a Solution
Is the reason because the sets of all nonsingular 3x3 matrices include those composed of complex numbers which are not reals and therefore the addition of such matrices, which all satisfy A1-A4, are not over the reals?