Find two nilpotent 2 by 2 matrices such that their sum is not nilpotent.

I have been trying a few matrices but none are working, is there a more logical, easier way to find these matrices? thanks.

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- Nov 8th 2008, 11:57 AMtttcomraderFind nilpotent
Find two nilpotent 2 by 2 matrices such that their sum is not nilpotent.

I have been trying a few matrices but none are working, is there a more logical, easier way to find these matrices? thanks. - Nov 8th 2008, 12:03 PMclic-clac
01 00

00 10

are nilpotent, but their sum,

01

10

is inversible so it is not nilpotent :) - Nov 8th 2008, 04:50 PMtttcomrader
So inversible means no nilpotent? How so? Thanks.

- Nov 8th 2008, 05:10 PMThePerfectHacker
Because if $\displaystyle A$ is invertible then $\displaystyle A^n$ is invertible. Thus, if $\displaystyle A^n$ is not invertible then $\displaystyle A$ is not invertible. If $\displaystyle A^n $ is zero matrix then it means $\displaystyle A^n$ is not invertible and so $\displaystyle A$ is not invertible.

- Jan 27th 2009, 07:22 AMarbolis