The total number of elements in a matrix is given by the product of its number of rows and columns:
\[
m \times n = 36,
\]
where \( m \) is the number of rows, and \( n \) is the number of columns.
To determine the possible orders of the matrix, find all pairs of positive integers \( (m, n) \) such that their product equals \( 36 \). These pairs are the factors of \( 36 \):
\[
(1, 36), (2, 18), (3, 12), (4, 9), (6, 6), (9, 4), (12, 3), (18, 2), (36, 1).
\]
There are \( 9 \) such pairs, corresponding to \( 9 \) possible orders of the matrix.
Hence, the number of possible orders is (D) 9.