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Let V be the space of n X n matrices over F. Let A be a fixed n X n matrix over F. Let T and U be the linear operators on V defined by T(B) = AB U(B)...

Let V be the space of n X n matrices over F. Let A be a fixed n X n matrix
over F. Let T and U be the linear operators on V defined by
T(B) = AB
U(B) = AB - BA.
(a) True or false? If ,2 is diagonalizable (over F), then T is diagonalizablc.
(b) True or false? If A is diagonalizable, then U is diagonalizablc.

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