(21) (12 points) Given the ellipse $C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ passes through the point $(0,1)$, and the eccentricity is $\frac{\sqrt{3}}{2}$.
(1) Find the equation of the ellipse $C$;
(2) Suppose the line $l: x=m y+1$ intersects the ellipse $C$ at points $A$ and $B$, and the point $A$ is symmetric to point $A^{\prime}$ about the $x$-axis (where $A^{\prime}$ does not coincide with $B$). Does the line $A^{\prime} B$ intersect the $x$-axis at a fixed point? If so, write down the coordinates of the fixed point and prove your conclusion; if not, explain why.