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## Homework Statement

Is U = {

**A**|

**A**[itex]\in[/itex]

^{n}ℝ

^{n},

**A**is invertible} a subspace of

^{n}ℝ

^{n}, the space of all nxn matrices?

## 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?