(a) Prove that every eigenvalue of a matrix A is also an eigenvalue of its transpose AT.
(b) Do they have the same eigenvectors? Prove that if v is an eigenvector of A with eigenvalue λ and w is an eigenvector of AT with a different eigenvalue μ ‰  λ, then v and w are orthogonal vectors with respect to the dot product.
(c) Illustrate this result when

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