Question: (a) Let A be an m n matrix. Show that the following are equivalent. (i) A has orthogonal rows. (ii) A can be factored

(a) Let A be an m × n matrix. Show that the following are equivalent.
(i) A has orthogonal rows.
(ii) A can be factored as A = DP, where D is invertible and diagonal and P has orthonormal rows.
(iii) 4AT is an invertible, diagonal matrix.
(b) Show that an n x n matrix A has orthogonal rows if and only if A can be factored as A = DP, where P is orthogonal and D is diagonal and invertible.

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