Answer :
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.
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