(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# (LinearAlgebra) all 2x2 invertible matrices closed under addition?

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