Question: Problem 3: a) Show that if A, B E Mn are not both singular then AB is nonderogatory if and only if BA is nonderogatory.

Problem 3: a) Show that if A, B E Mn are not both singular then AB is nonderogatory if and only if BA is nonderogatory. b) Give an example of A, B such that one of AB and BA is nonderogatory and the other is not. (Hint: Consider a 2 x 2 Jordan block and a diagonal matrix. )

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