For what values of \( n \) does there exist complex \( n \times n \) matrices \( A, B \) such that

\[ A B - BA = Id? \]

For what values of \( n \) does there exist complex \( n \times n \) matrices \( A, B \) such that

\[ A B - BA = Id? \]

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TopNewestIf d=0, the condition holds trivially for all n by taking A=B=I. If d is different from zero, taking trace of both sides and using the fact that tr(AB)=tr(BA), we conclude that none such n exists. – Abhishek Sinha · 1 year, 9 months ago

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– Calvin Lin Staff · 1 year, 9 months ago

Id means identity matrix.Log in to reply

– Abhishek Sinha · 1 year, 9 months ago

Anyways, I took it as identity matrix times the scalar d.Log in to reply

Notation for identity matrix isn't standardized anyway. I was debating between I and Id. – Calvin Lin Staff · 1 year, 9 months ago

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