For a matrix A, define the eigen-vector as a non-zero column matrix X and eigen-value a scalar › such that AX AX. (a) Prove that the eigen-values of a symmetric matrix are real. (b) Prove that the eigen-values of a skew-symmetric matrix are 0 or purely imaginary. (c) Find the absolute value(s) of the eigen-values of an orthogonal matrix.

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Q: Eigenvalues of an invertible matrix are nonzero. Justify your answer.

A: answer is yes detailed explanation is given below

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