I've got a question like this:

Let V be a finite dimensional vector space with dimV >= 2 . Show

that there exists a linear transformation T:V to V such that T not equal to zero but

T^2 = 0 .

I have figured out the "T not equal to zero but T^2 = 0 ." part already, rankT>=1, dimNulT>=rankT>=1, satisfies with dimV>=2 by rank theorem, but how to present it nicely?

Let V be a finite dimensional vector space with dimV >= 2 . Show

that there exists a linear transformation T:V to V such that T not equal to zero but

T^2 = 0 .

I have figured out the "T not equal to zero but T^2 = 0 ." part already, rankT>=1, dimNulT>=rankT>=1, satisfies with dimV>=2 by rank theorem, but how to present it nicely?

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