Let U be a linear operator in a dimensionally finite vector space V. Prove the following [closed]
Solution 1:
If $x\in N(U)$, $Ux=0$ and then $U^2(x)=U(Ux)=U(0)=0$ so $x\in N(U^2)$
Just generalize this.
If $x\in N(U)$, $Ux=0$ and then $U^2(x)=U(Ux)=U(0)=0$ so $x\in N(U^2)$
Just generalize this.