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Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. A matrix A Rx with n

Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. A matrix A Rx with n real orthonormal eigenvectors is symmetric. 2. Assume that w0 is an eigenvector for matrices A, BE Rxn, then AB - BA is not invertible. 3. If the Jordan canonical form of A is J, then that of A2 is J.

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