Example 2 If a matrix has 8 elements, what are the possible orders it can have Solution We know that if a matrix is of order m × n, it has mn elements Thus, to find
all possible orders of a matrix with 8 elements, we will find all ordered pairs of natural
numbers, whose product is 8 Thus, all possible ordered pairs are (1, 8), (8, 1), (4, 2), (2, 4)
Hence, possible orders are 1 × 8, 8 ×1, 4 × 2, 2 × 4
Example 3 Construct a 3 × 2 matrix whose elements are given by 
1 |
3 |
2
aij
i
j
=
−