Let $F$ be a field, with $\text{char}(F) = 0$, and $A \in M_{n\times n}(F)$ with $\text{tr}(A) = 0$. Show that there are matrices $B,C \in M_{n\times n}(F)$ that $A = BC - CB$.
2026-04-01 03:32:42.1775014362
Can we write a matrix with zero trace as a commutator?
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