3. If the function $y=k x(k>0)$ intersects with the function $y=\frac{1}{x}$ at points $A$ and $C$, and $A B$ is perpendicular to the $x$-axis at point $B$. Then the area of $\triangle A B C$ is ( ).
(A) 1
(B) 2
(C) $k$
(D) $k^{2}$
3. (A).

Let $A(x, y)$, then $x y=1$, so $S_{\triangle A B O}=\frac{1}{2} x y=\frac{1}{2}$. Since $\triangle A B O$ and $\triangle C B O$ have the same base and height, therefore, $S_{\triangle A B C}=2 \times S_{\triangle A B O}=1$.