True Or False:

1) The set of invertible 2x2 matrices is a subspace of M2x2(F)

2)Every bijective function is one-to-one

Question

True Or False:

1) The set of invertible 2x2 matrices is a subspace of M2x2(F)

2)Every bijective function is one-to-one

jamesj · Answer

A subspace must contain the zero vector.  Is that the case?

By definition a bijective function is ...

jamesj · Answer

making sense?

anonymous · Answer

I understand that a subspace has a zero vector but the zero matrix isn't invertible so its not a part of the set of invertible matrix.

The definition of a bijective function is one-to-one AND onto. So I figured its false since it contains both properties and not just one of them.

jamesj · Answer

a) Right.  And hence it is not a subspace.

b) Think again.  If X has properties A and B, then it is true that X has property A by itself and it is true that X has property B by itself.  If an elephant is a grey animal, then yes it is true that "an elephant is an animal" and "an elephant is grey"

anonymous · Answer

oh ok lol makes total sense, thanks...