Invertible 3x3 matrices a subspace of 3x3 matrices

[wumple]

Homework Statement

Is the set of invertible 3x3 matrices a subspace of 3x3 matrices?

Homework Equations

The Attempt at a Solution

I think no - the 'neutral 0 element' is not in the subset since the 3x3 0 matrix is not in the subset. Am I right? The book says it's not a subspace because it's not closed under addition, but I'm not sure if my reason is also correct.

 

[Dick]

Your reason is also correct.

 

[wumple]

thanks! also, quick question: does the 'neutral 0 element' mean the additive identity?

 

[Dick]

thanks! also, quick question: does the 'neutral 0 element' mean the additive identity?

Sure, subspace generally means closed under linear combinations. The zero matrix is the identity.