True or false a quadrilateral is a square if and only if it is a rhombus and rectangle

True

Step-by-step explanation:

A quadrilateral is any polygon with 4 sides. It can be a square, rhombus, rectangle, parallelogram etc.

A rhombus is a parallelogram with all sides equal and the diagonals cut each other equally at right angles.

A rectangle is a parallelogram with opposite sides equal and all internal angles is at right angles. The diagonals are congruent and divided the rectangle into equal halves.

A square is a parallelogram with all sides equal and all angles equal to 90°.

Thus square fulfills the property of a rhombus and a rectangle.

Thus, if a quadrilateral which is a rhombus and a rectangle can only be a square.