True/false. Give a brief explanation/counterexample for each part. (i) The eigenvalues of a square matrix A and its transpose A" are always the same. (ii) If v E R" is

an eigenvector for A E R"Xn, then v is also an eigenvector for A-1. (iii) If A and B are n × n diagonalizable matrices, then A+B is also diagonalizable. (iv) If A and B are orthogonal n by n matrices, then AB is also orthogonal. (v) If A E R²x² is not diagonalizable, then A? is not diagonalizable.

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