Let a be an n x n matrix and c be a nonsingular matrix of
1. Suppose that tr(PA) = 0 for every skew-symmetric matrix P. Show that the matrix A is symmetric.
2. Let A be an n X n matrix and C be a nonsingular matrix of order n X n. Show that A, C-1 AC, and CAC-1 have the same set of eigenvalues.
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