Question: Suppose that A and B are square matrices, and that C = AB (as defined on the previous assignment). (a) Let p A be the

Suppose that A and B are square matrices, and that C = AB (as defined on the previous assignment). (a) Let p_A be the minimal polynomial of A, and similarly for p_B and p_C . Prove that if f(x) is any polynomial then p_C divides f if and only if p_A and p_B both divide f. (b) Give an example to show that it is possible to have p_C (x) /= p_A(x)p_B(x). (/= means not equal)

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