Nilpotent matrix proof

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johnsmith12358

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Dec 10, 2020
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Let A be a 3 x 3 matrix. Prove that if there exists n > 3 such that A^n= 0, then A^3 = 0. Can someone help me prove this statement. I'm thinking that since A is nilpotent, its only eigenvalue is 0. That implies that (A^3)v=(lambda^3)v=0, which implies that A^3=0.
 
Try induction. Also do not post your question in multiple forums. It is not fair to the volunteers who spend time posting hints when the solutions has already reached on another forum.
 
I posted this question in the hopes of receiving a multitude of perspectives to help me reach my own understanding. Isn't that why these forums exist? Your statement seems to imply such forums are simply a race to see who can reach the "solution" first. If that were the case, then they'd be rather dull. Would they not?
 
It is not fair for the other users of this forum to have to wait longer to receive help because helpers on this forum are trying to help you even though you (may) have already received your answer. What makes you think that you would not have received multitude of perspective from the many helpers on this forum? Maybe you did not realize the point I just made but to me and many other helpers here feel that what you did is selfish.

Actually I (we) feel that you seem to imply such forums are simply a race to see who can reach the "solution" first which is better for you with complete disregard to the other students. If you do not realize that then it is sad.
 
Given the response (or lack thereof) I received on this forum, I don't think my question "distracted" anyone from helping others. What is truly sad is your insistence on criticizing a new member for asking an honest question in a manner you deem unacceptable. Further, I find your suggestion that these forums should be siloed off from each other quite silly. Are we really supposed to believe there is no overlap in questions between this forum and others of a similar kind? To put it another way, would you criticize someone for asking a question here that has already been answered on a different forum? If not, then why?

Now, I'm sure you will insist that the difference is that I asked a question on multiple forums, but I challenge you to consider whether the effect of these two actions is different. In both cases, helpers are devoting time to a question that the individual could have found an answer to elsewhere. Finally, ask yourself this: was it rude and perhaps selfish of me to criticize a new member without any knowledge of their understanding of forum etiquette and not even attempt to offer a helpful answer to his/her question?
 
We do not offer answers on this forum. We offer help. I did suggest that you use induction. If that hint was not enough I or someone else here would have given you another hint.
 
Indeed, if you take the time to read my question, you will note that I asked for "help" proving the statement. What you offered was mostly criticism. Regardless, this exchange has become tedious and I suggest we both move on.
 
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