Step 1: Use the pH and OH\(^-\) concentration relationship.
We know that for a weak base, \( pH + pOH = 14 \). The pH is given as 11.2, so we calculate pOH:
\[
pOH = 14 - pH = 14 - 11.2 = 2.8
\]
Next, the OH\(^-\) concentration is given by:
\[
[OH^-] = 10^{-pOH} = 10^{-2.8} = 1.585 \times 10^{-3} \text{ mol dm}^{-3}
\]
Thus, the correct answer is (A).