Let \(M\) be \(3\times 3\) matrix over \(\mathbb {C}\) with \(\operatorname {trace}(M^k)=0\) for \(k=1,2,3\). Prove that \(M\) is nilpotent.
Question
Math 6310 • Algebra
Spring 2015 • Question 6
Question
Spring 2015 • Question 6
Let \(M\) be \(3\times 3\) matrix over \(\mathbb {C}\) with \(\operatorname {trace}(M^k)=0\) for \(k=1,2,3\). Prove that \(M\) is nilpotent.