P: 88 I can't make sense of your expression, how does adding two vectors get you a 2x2 matrix? Are you confusing something here, or am I the confused one? Anyway, if the additive identity does not hold, you're not dealing with a vector space and all bets are off (as far as linear algebra is concerned). One of the requirements of a vector space $$V$$ is that there exists an element $$\mathbf{0} \in V$$ such that $$\mathbf{v} + \mathbf{0} = \mathbf{v}$$ for all $$\mathbf{v} \in V$$.