Is the set of all 2x2 invertible matrices with the standard matrix addition and scalar multiplication under vector space?

Question

perl · Answer

under vector matrix?

anonymous · Answer

Yes, thanks but can you help me with proving some axioms?

perl · Answer

ok

anonymous · Answer

1,4,5,6 and 10.

anonymous · Answer

attachment

perl · Answer

ok, the sum of two invertible matrices is also an invertible matrix

anonymous · Answer

should i use actual values or arbitrary terms like a11, a12, a21, a22?

perl · Answer

you could

perl · Answer

so an invertible matrix has a non-zero determinant

perl · Answer

i think you can use this fact

anonymous · Answer

yes, that's correct but which do you suggest, actual numbers or arbitrary terms?

perl · Answer

give me a moment

amistre64 · Answer

do you want to prove if for one particular matrix or all of them in general?

dan815 · Answer

no

anonymous · Answer

I've attached an image, i'm focusing on axiom 1,4,5,6 and 10 since those are the critical axioms.

amistre64 · Answer

right, but do you want to prove it for some specific 2x2 or for 2x2 in general?

anonymous · Answer

that's the question i asked @perl  earlier. wether it should be actual terms or for any where i would use terms like a11, a12, a21, a22

dan815 · Answer

the 
[0  0]
[0  0] matrix is not invertible

amistre64 · Answer

your post says the set of all 2x2 matrixes right?  so we dont want to be specific about out values

anonymous · Answer

@dan815 , the question defined its parameters and includes invertible matrices.

perl · Answer

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