It is known that if a matrix is of the order m × n, then it has mn elements.

Therefore, to find all the possible orders of a matrix having 24 elements, we had to find all the ordered pairs of natural numbers whose product is 24.

The ordered pairs are: (1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), and (6, 4).

Therefore, the possible orders of a matrix having 24 elements are;

1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, 6 × 4

(1, 13) and (13, 1) are the ordered pairs of natural numbers whose product is 13.

Therefore, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.