prove $\displaystyle Null(A)\subset Null(A^2)$
I just don't know how to tackle this problem without making a computational mess. Can anyone tell me what's the trick? please
Well if $\displaystyle x \in \mbox{Nullspace }(A) $, then $\displaystyle Ax=0$, so also $\displaystyle A^2x = A(Ax)=A(0)=0$, so $\displaystyle x \in \mbox{Nullspace }(A^2) $. Therefore $\displaystyle \mbox{Nullspace }(A) \subset \mbox{Nullspace }(A^2) $.