Question: Please help on these 3 problems. Thank you. 1. A permutation matrix P is a matrix such that there is exactly one 1 in every

Please help on these 3 problems. Thank you.

1. A permutation matrix P is a matrix such that there is exactly one 1 in every row and every colum and all other entries are zeros. Show that every permutation matrix is orthogonal. 2. Let Q E Rmix" be a matrix. If (Qr, Qy) = (x, y) for all x, y e R", show that Q is isometric, i.e., show that Q Q = In. 3. Find a rotation matrix Q such that 2 12 - -13

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