let A be nxn matrix.

Prove:

1. if A^2 = 0 so A columns are vectors in the solution space of the system Ax=0, and that the matrix deg is <= to n/2.

2. if deg(A^2)<deg(A), so to Ax=0 there is non trivial solution and that to A^2x=0 there is y that Ay =/ 0 (Ay is not equal to zero).

thanks ahead