# Complex matrices with null trace [duplicate]

I'm trying to prove the following:

Let $A\in \mathbb{C}^{n\times n}$ be a matrix with null trace; then $A$ is similar to a matrix $B$ such that $B_{jj}=0$ (i.e. it has zeroes on its diagonal).

Any ideas? Induction on $n$ sounded feasible but I wasn't able to put together anything.

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## marked as duplicate by Marc van LeeuwenFeb 9 at 12:32

I'm going to perform the unusual move of closing this old question as a duplicate of a recent question. The reason for doing so rather than the other way round is that the other question both is more general (nothing else about the field is needed than having characteristic$~0$), and has a self-contained answer, whereas this one only has a link-only answer. –  Marc van Leeuwen Feb 9 at 12:32