A square is a figure with four equal sides and four right angles.In a square the diagonals bisect at right angles .
In the above given options option A is the right answer.
If the diagonals of any parallelogram are perpendicular then the figure is not necessarily a square.
Diagonals are perpendicular in a rhombus too.
A square and Rhombus both have diagonals that are perpendicular.
So it is not a necessary condition for a parallelogram to be a square .
The other options are right .
So option B is the right option that if diagonals are perpendicular is not sufficient to prove the figure to be a square.