0
$\begingroup$

Suppose V is vector space and S,T ∈ L(V,V) are such that range(S) ⊂ ker(T).

Prove (ST)(ST) = 0

Now, I know that this means that if you apply the linear transformation S to any v in V, then you get S(v) = 0. Apart from that, I am a little stuck as to how I should solve this problem... Any help would be appreciated!

  • 0
    range(S)$\subset$ker(T) means that T annihilates everything in the image of S. so you have $TS=0$, which means $(ST)(ST)=S(TS)T=0$ – 2017-02-02
  • 0
    The thing I'm struggling to understand is how is TS defined? Are you multiplying both linear transformations? – 2017-02-02
  • 0
    Nevermind, I got it! Thank you :) @DavidHolden – 2017-02-02

0 Answers 0