help with some general proofs and other questions involving vector spaces

Determine wether the set, together with the indicated operations, is a vector space. If not identify atleast one of the ten vector space axioms that fail.

#1

The set of all 2x2 matrices of the form with the standard operations.

#2

The set of all 2x2 nonsingular (invertable or non zero determinant) with the standard operations.

I've wracked my brains with these for well over an hour now and made little to no progress... my book is of little to no help.

Thanks in advance for anyone that can help! (Hi)