# Linear Algebra: Prove that the set of invertible matrices is a Subspace

1. Jan 27, 2013

### Millacol88

1. The problem statement, all variables and given/known data
Is U = {A| A $\in$ nn, A is invertible} a subspace of nn, the space of all nxn matrices?

3. The attempt at a solution
This is easy to prove if you assume the regular operations of vector addition and scalar multiplication. Then the Identity matrix is in the set but 0*I and I + (-I) are not, so its not closed under vector addition or scalar multiplication. Is there a way to prove this without assuming the usual vector operations?

2. Jan 27, 2013

### Dick

Not until they tell you what the alternative addition and multiplication operations are. I don't think you have to worry about that. Your examples are just fine.