A condition ensuring diagonalizability
Suppose
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Suppose $F$ is a field and $A$ is an $n\times n$ matrix over $F$. Suppose further that $A$ possesses distinct eigenvalues $\lambda_1$ and $\lambda_2$ with $\dim \operatorname{Null}(A-\lambda_1 I_n)=n-1$. Prove $A$ is diagonalizable.