Each of the following (with the usual operations of addition and multiplication) fails to be a ring. In each case, you should prove this by showing one of the ring axioms

which is not satisfied.

1) N, the set of natural numbers.

2) 2Z+1, the set of odd integers.

3) The set of invertible 22 real matrices.

4) The set of polynomials in which the coefficient of x3 is zero.

5) The set of vectors in real 3-dimensional space (the multiplication here is cross product).

am not able to start doing this question at all.. It would be helpful if some one could show me how to do part (1), so that I could follow up on doing the other parts... help wpuld be appreciated thanks