Show that any zero trace matrix is similar to a null diagonal matrix.
let $A=(a_{i,j})_{1 \leq i,j \leq n} \in M_n(K)$ such that $ \sum_{k=1}^{n} a_{k,k}=0$ I need to show that that there is $P \in Gl_n(K)$ such that $B=P^{-1}AP$ such that $diag(B)=(0,...,0)$ diag means coefficients on the diagonal of B .