​$$Let \ A\ \text{ be an } n \times n \text{ matrix such that the set of all its nonzero}\\ \text{eigenvalues has exactly r elements.}\\\text{ Which of the following statements is true?}$$​​

Correct option is C

​$$\text{Order of } A \text{ is } n \text{ and it has } r \text{ non-zero eigenvalues, so} \\\text{Algebraic multiplicity (A.M.) of eigenvalue } 0 \text{ of } A = n - r \\\implies \text{Geometric multiplicity of eigenvalue } 0 \text{ of } A = n - \text{rank}(A) \leq \text{A.M.} \\\implies n - \text{rank}(A) \leq n - r \\\implies \text{rank}(A) \geq r$$​​