Let X be a n-square matrix such that Y = X + 8I. Which of the following property will exist?(a) idempotent(b) Y transpose is nilpotent(c) X nilpotent(d) Y inverseThe question was posed to me during an interview.This intriguing question originated from Permutation Groups topic in division Groups of Discrete Mathematics

Let X be a n-square matrix such that Y = X + 8I. Which of the followin

1.	Let X be a n-square matrix such that Y = X + 8I. Which of the following property will exist?(a) idempotent(b) Y transpose is nilpotent(c) X nilpotent(d) Y inverseThe question was posed to me during an interview.This intriguing question originated from Permutation Groups topic in division Groups of Discrete Mathematics
Answer» The CORRECT option is (b) Y TRANSPOSE is nilpotent The explanation: Suppose, we have a matrix \(a=\begin{bmatrix} 1 & 0\\ 2 & 1\\ \end{bmatrix} \) then Y^2 will not resulting in Y, hence it is not IDEMPOTENT, Y^2 is not 0 and so it is not nilpotent. But, as Y is a square matrix, by the property inverse will exist in this case.

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