Let A be an m x n matrix with rank(A) = r. If P and Q are invertible m x m and n x n matrices, respectively, show that: (a) rank(AQ) = r, (b) rank(PA) = r, and (c) rank(PAQ) = r.
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Since P is an m x m matrix and Q is an n x n matrix, both are square matrices. If they are invertible, then their determinants are non-zero. So, we need to show that det(P) ≠ 0 and det(Q) ≠ 0. Show more…
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