Given below are some pairs of statements. Combine each pair using if and only if :

(i) p : If a quadrilateral is equiangular, then it is a rectangle.

q : If a quadrilateral is a rectangle, then it is equiangular.

(ii) p : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

(iii) p : A quadrilateral is a parallelogram if its diagonals bisect each other.

q : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

(iv) p : If f(a) = 0, then (x – a) is a factor of polynomial f(x).

q : If (x – a) is a factor of polynomial f(x), then f(a) = 0.

(v) p : If a square matrix A is invertible, then |A| is nonzero.

q : If A is a square matrix such that |A| is nonzero, then A is invertible.