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Questions about rank and eigenvalues of a matrix
Let $A=\begin{pmatrix}1&w&w^2\\w&w^2&1\\w^2&w&1\end{pmatrix}$ Where $w$ is a complex no. s.t. $w^3=1$. Its clear by adding columns of matrix that $0$ is an eigen value of $A$.
Do there exist linearly independent vectors $u,v\in\mathbb{C}^3$ s.t. $Au=Av=0$?
can anyone help me please....