Hi, I have trouble understanding vector space and how to determine whether something is a vector space or not. I am having trouble with these problems.

Determine whether the set, together with the indicated operations, is a vector space. If not, identify at least one of the ten vector space axioms that fails.

1) M sub 1,1 ( I guess it's a matrix 1x1?)

2) the set of all fifth degree polynomials with the standard operations

3) the set of all first degree polynomial functions ax+b, a is not equal to 0, whose graphs pass through the origin with the standard operations.

Please help. Thank you.