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Let A, B be complex nxn matrices. Which of the following statements are true? If A, B and A + B are invertible, then

Let A, B be complex nxn matrices. Which of the following statements are true? If A, B and A + B are invertible, then A+B is invertible. If A, B and A + B are invertible, then B is invertible. If AB is nilpotent, then BA is nilpotent. Characteristic polynomials of AB and BA are equal if A is invertible.

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