Let A Rmn, B Rnr, and C = AB. Show that (a) If A and

Question:

Let A ∊ Rm×n, B ∊ Rn×r, and C = AB. Show that
(a) If A and B both have linearly independent column vectors, then the column vectors of C will also be linearly independent.
(b) If A and B both have linearly independent row vectors, then the row vectors of C will also be linearly independent.