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A be a n-square matrix with integer entries and B = A + 12 I. Then

(a) B is idempotent      (b) B inverse exist
(c) B is nilpotent       (d) B inverse is idempotent

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answer is (c)

let a=[1 2

         3 4] then B^2 will not be B hence not idempotent, B^2 is not 0 so not nilpotent but as B is a square matrix so we can find inverse.

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