If i = √-1, then how many values does i^-2n have for different n ∈ ℤ?

If $x = \frac{a}{b-c}$, $y = \frac{b}{c - a}$, $z = \frac{c}{a - b}$ then what is the value of the following?

$\begin{vmatrix} 1 & -x & x\\ 1 & 1 & -y\\ 1 & z & 1 \end{vmatrix}$

Consider the following in respect of the matrix $\rm A = \begin{bmatrix} 1 & 1 & 1\\ 1 & 1 & 1\\ 1 & 1 & 1 \end{bmatrix}$

1. Inverse of A does not exist

2. A³ = A

3. 3A = A²

Which of the above are correct?

Direction: Consider the following for the next two (02) items that follow.

A circle is passing through the points (5, -8), (-2, 9) and (2, 1).

What are the coordinates of the center of the circle?