Question: Let A Rmn, B Rnr and C = AB. Show that (a) The column space of C is a subspace of the column

Let A ∊ Rm×n, B ∊ Rn×r and C = AB. Show that
(a) The column space of C is a subspace of the column space of A.
(b) The row space of C is a subspace of the row space of B.
(c) rank(C) ≤ min{rank(A), rank(B)}.

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