Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. A matrix Aε Rnxn

Question

Are the following statements true or false? If true, prove the statement. If false, give a counterexample.
1. A matrix Aε Rnxn with n real orthonormal eigenvectors is symmetric.
2. Assume that w =! 0 is an eigenvector for matrices A, B v Rnxn, then AB - BA is not invertible.
3. If the Jordan canonical form of A is J, then that of A² is J².

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