LetA1 D% 21 !32 &; A2 D% 13 !1 !2&; B D%24 12 &: (a) Show that A1B D A2B and note that
Chapter 5, Problem 6(choose chapter or problem)
LetA1 D% 21 !32 &; A2 D% 13 !1 !2&; B D%24 12 &: (a) Show that A1B D A2B and note that A1 A2. Thus the cancellation law does not hold for matrices; that is, if A1B D A2B and B 0, it does not follow thatA1 D A2. (b) Let ADA1!A2 and use part (a) to show that ABD0. Thus the product of two nonzero matrices may be the zero matrix.
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