Let T: R5 → R5  be a linear operator whose characteristic polynomial is pT(x) = (x−3)3(x−5)2. Let V3 and V5 be the eigenspaces associated with eigenvalues ​​3 and 5, respectively. Judge each item below as true or false. (A) If dimV3 = dimV5, then T is diagonalizable (B) If T is diagonalizable, then there is a basis B of R5 formed by eigenvectors such that det([T]BB) = 675. (C) If V3 is generated by v1,v2 ∈ R5 and V5 is generated by u1, u2 ∈ R5, then T is not diagonalizable.

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