Distinct eigenvalues and linear independence

Let A| be a n x n matrix. 1. Suppose that A has n distinct eigenvalues A1, . .., An, and corresponding non-zero eigenvectors X1, . . ., Xn. Prove that {x1, ..., Xn} is linearly independant. Hint: You may use without proof the following property: If {y1, ...,ym} is linearly dependent then there exists some p such that 1