Correct answer: (B) K is nilpotent.; (C) I+K is invertible.
Explanation
The commutator of two upper-triangular matrices is strictly upper triangular, with zero diagonal. Thus K is similar to N with N³=0, proving B. Then $(I+K)^{-1}=I-K+K^2$, proving C. A fails since all eigenvalues are zero; a diagonalizable nilpotent matrix must be zero, refuting D for nonzero K. **B,C**.
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