Question

If a matrix has 24 elements, what are the possible orders it can have?

Answer 1

A matrix of order m × n has mn elements.

We first find out all the ordered pairs, the product of whose elements is 24.

Hence, all possible ordered pairs are:

(1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), (6, 4).

∴ The possible orders of the matrix are:

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