Question: Permutation Matrix A permutation metric}: is a square matrix that has exactly a single 1 in every row and column, and zeros elsewhere. For example,

Permutation Matrix

A permutation metric}: is a square matrix that has exactly a single 1 in every row and column, and zeros elsewhere. For example, 0 1 0 0 1 0 0 0 0 O O 1 0 0 1 0 Let P be an arbitrary n X n permutation matrix. 1. Prove that P is always invertible. 2. Prove that PT is a permutation matrix

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