Consider the matrix \( A \) below: \[ A = \begin{bmatrix} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{bmatrix} \] For which of the following combinations of \( \alpha, \beta, \) and \( \gamma \), is the rank of \( A \) at least three? (i) \( \alpha = 0 \) and \( \beta = \gamma \neq 0 \).
(ii) \( \alpha = \beta = \gamma = 0 \).
(iii) \( \beta = \gamma = 0 \) and \( \alpha \neq 0 \).
(iv) \( \alpha = \beta = \gamma \neq 0 \).