Assume $T$ is an operator on $\mathbb R^3$, $$B=\{(1, 1, 1)^T, (1, -1, 0)^T, (0, 1, -1)^T\}$$ is a basis of eigenvectors for $T$ and that the corresponding eigenvalues of $T$ are the real numbers $a$, $b$, $c$. Prove that $T$ is self adjoint if and only if $b=c$. Thanks!
Proof about self-adjoint operator
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linear-algebra