Question

If a matrix has 10 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 10.

Hence, all possible ordered pairs are:

(1, 10), (10, 1), (2, 5), (5, 2).

∴ The possible orders of the matrix are:

1 × 10, 10 × 1, 2 × 5, 5 × 2.