2. Given that the origin is inside the ellipse $k^{2} x^{2}+y^{2}-4 k x+2 k y+k^{2}-1=0$, the range of the parameter $k$ is
(A) $|k|>1$;
(B) $|k| \neq 1$;
(C) $-1<k<1$;
(D) $0<|k|<1$.
2. (D)

A point outside the ellipse can be far from the origin, with the absolute values of its coordinates $x, y$ being very large, making the left side of the equation greater than 0. Therefore, the coordinates of internal points make the left side of the equation less than 0. Substituting the coordinates of the origin into the left side of the equation gives
$$
k^{2}-1<0,
$$

and $k \neq 0$, (otherwise the equation does not represent an ellipse), so the answer is (D).