Show that the matrix a is symmetric

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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.

Reference no: EM131369021

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