Question: 3) Let A be an n n matrix over F whose characteristic polynomial splits and is given by: f(t) = det(A - tI) =

3) Let A be an n n matrix over F whose characteristic

3) Let A be an n n matrix over F whose characteristic polynomial splits and is given by: f(t) = det(A - tI) = (1)"(t 1) ( 2) ... ( n) (we're not assuming that X's are distinct). (a) Show that det(A) = A A2... An.

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