Consider the matrix

$$P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$$

The number of distinct eigenvalues

1. $0$
2. $1$
3. $2$
4. $3$

There will be 3 Eigen values which are 1,1,1. All of these are same so the no of distinct Eigen values will be 1.

Right answer will be option  (B) 1
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Question asks 'The number of distinct eigenvalues'? 1,1,1 so no one is distinct. Answer should be 0 but all answers over internet and book says 1 which is confusing to me. 1 is similar to 1 and another 1. So no distinct eigenvalues. Thus 0.