1. The problem statement, all variables and given/known data Suppose V is a vector space. Is the set of all 2x2 invertible matrices closed under addition? If so, please prove it. If not, please provide a counter-example. 2. Relevant equations 3. The attempt at a solution well i know that what does it mean to be closed under addition. When V is closed under addition, if I suppose vector u and w are in the V, their addition u+w is also in the V, right? The answer for the question is No. A counter-example my professor provided is I+(-I)=0 I and (-I) are invertible, but their addition 0 is not invertible. and I know why it's not invertible. But I don't figure out why it is not closed under addition,,. If the addition is not invertible, does it mean that the addition is not in the V?