To solve the equation \( x^2 = 81 \) using inspection, we can take the square root of both sides.
The solutions to this equation are:
\[ x = \sqrt{81} = 9 \] and \[ x = -\sqrt{81} = -9 \]
Thus, the complete solution set is:
\[ {-9, 9} \]
The correct option is:
A. {-9, 9}