A matrix P R n,n is a permutation matrix if its columns are a permutation of

Question:

A matrix P ∈ R^n,n is a permutation matrix if its columns are a permutation of the columns of the n x n identity matrix.
1. For a n x n matrix A, we consider the products PA and AP. Describe in simple terms what these matrices look like with respect to the original matrix A.

2. Show that P is orthogonal.

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