1. The problem statement, all variables and given/known data The set of all nonsingular 3x3 matrices does not form a vector space over the real numbers under addition. Why? 2. Relevant 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 3. 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?