The hint that was given was to prove that ST^n-T^nS = nT^n-1 (which I did) and see how it bring about a contradiction, but I don't see how the second part works.
Homework Statement
Let V = F^n
for some n ≥ 1. Show that there do not exist linear maps
S, T : V → V such that ST − T S = I.
The Attempt at a Solution
I used induction to prove that ST^n-T^nS = nT^n-1 and that S^nT-TS^n=nS^n-1, and I know I'm supposed to use that to come up with a...
Homework Statement
One of the questions on my Algebra assignment is as follows.
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